There is nothing old about the Jewish Bible!

Jews calls their Bible Tanakh. The Tanakh also Tenakh, Tenak, Tanach) or Mikra or Hebrew Bible is the canonical collection of Jewish texts, which is also a textual source for the Christian Old Testament. These texts are composed mainly in Biblical Hebrew, with some passages in Biblical Aramaic (in the books of Daniel, Ezra and a few others). The traditional Hebrew text is known as the Masoretic Text.

The Tanakh consists of twenty-four books: it counts as one book each Samuel, Kings, Chronicles and Ezra–Nehemiah and counts Trei Asar (תרי עשר, the Twelve Prophets; literally "twelve") as a single book.

The books are
Torah - The Pentateuch

Bereishit - Genesis
Shemot - Exodus
Vayikra - Leviticus
Bamidbar - Numbers
Devarim - Deuteronomy

Nevi'im - Prophets

Yehoshua - Joshua
Shoftim - Judges
Shmuel I - I Samuel
Shmuel II - II Samuel
Melachim I - I Kings
More »
Melachim II - II Kings
Yeshayahu- Isaiah
Yirmiyahu - Jeremiah
Yechezkel - Ezekiel
Hoshea - Hosea
Yoel - Joel
Amos
Ovadiah - Obadiah
Yonah - Jonah
Michah - Micah
Nachum - Nahum
Chavakuk - Habakkuk
Tzefaniah - Zephaniah
Chaggai - Haggai
Zechariah
Malachi

K'tuvim - Scriptures

Tehillim - Psalms
Mishlei - Proverbs
Iyov - Job
Shir Hashirim - Song of Songs
Rut - Ruth
More »
Eichah - Lamentations
Kohelet - Ecclesiastes
Esther
Daniel
Ezra
Nechemiah - Nehemiah
Divrei Hayamim I - I Chronicles
Divrei Hayamim II - II Chronicles

Self respecting Jews will NEVER call the Tanakh the Old Testament! There is nothing old about it! The covenant between G-d and his people the Jews is not old, it is an everlasting covenant.

Yirmiyahu - Jeremiah - Chapter 31
30 Behold, days are coming, says the Lord, and I will form a covenant with the house of Israel and with the house of Judah, a new covenant.
31 Not like the covenant that I formed with their forefathers on the day I took them by the hand to take them out of the land of Egypt, that they broke My covenant, although I was a lord over them, says the Lord.
32 For this is the covenant that I will form with the house of Israel after those days, says the Lord: I will place My law in their midst and I will inscribe it upon their hearts, and I will be their God and they shall be My people.
33 And no longer shall one teach his neighbor or [shall] one [teach] his brother, saying, "Know the Lord," for they shall all know Me from their smallest to their greatest, says the Lord, for I will forgive their iniquity and their sin I will no longer remember.
34 So said the Lord, Who gives the sun to illuminate by day, the laws of the moon and the stars to illuminate at night, Who stirs up the sea and its waves roar, the Lord of Hosts is His name.

Jews who respect their own faith and their own Hebrew Scriptures should never refer to their own Scriptures as the 'Old Testament.

Jeremiah 31:30 speaks of a 'new covenant.' But one could ask the question, 'is this new covenant a covenant which replaces any of the covenants that G-d made with the Jews beforehand?

When G-d makes a new covenant with the Jews, it is only to re-establish and re-affirm the covenants with the Jews that came before. The covenant G-d made with Isaac did not replace or break the covenant G-d made with Abraham. The covenant that G-d made with Jacob did not replace or break the covenant G-d made with Isaac or with Abraham. One example of this can be seen in Leviticus 26:42, where the Jews were told in the verses just before verse 42 that when they sin, they will be punished for their sins, but then they are told that G-d's covenant with them is eternal:

Vayikra - Leviticus - Chapter 26
39 And because of their iniquity, those of you who survive will rot away in the lands of your enemies; moreover, they will rot away because the iniquities of their fathers are still within them.
40 They will then confess their iniquity and the iniquity of their fathers their betrayal that they dealt Me, and that they also treated Me as happenstance.
41 Then I too, will treat them as happenstance and bring them [back while] in the land of their enemies. If then, their clogged heart becomes humbled, then, [their sufferings] will gain appeasement for their iniquity,
42 and I will remember My covenant [with] Jacob, and also My covenant [with] Isaac, and also My covenant [with] Abraham I will remember. And I will remember the Land,

Had the covenants that G-d made with Isaac and Abraham been made null and void by the covenant G-d made with Jacob, there would have been no need to have specified the covenants G-d had made with Isaac and Abraham in the verse above.

The covenant that G-d made with the People of Israel through Moses did not replace or break the covenant G-d made with Jacob, or with Isaac, or with Abraham. Every subsequent covenant that G-d makes with the Jews re-affirms and re-establishes the covenant that G-d made with the Jews before it.

The covenant that G-d made with the Jews is an eternal covenant, and it is a covenant made with them, with their descendants, and with all those who convert to Judaism. G-d's promise to the Jews, that His covenant with them is eternal, is repeated over and over again throughout the Hebrew Scriptures. Here are just a few examples:

Bereishit - Genesis - Chapter 17
7 And I will establish My covenant between Me and between you and between your seed after you throughout their generations as an everlasting covenant, to be to you for a God and to your seed after you.
8 And I will give you and your seed after you the land of your sojournings, the entire land of Canaan for an everlasting possession, and I will be to them for a God."

See also Genesis 17:12-13, Genesis 17:19

Tehillim - Psalms - Chapter 105
6 The seed of Abraham His servant, the children of Jacob, His chosen ones.
7 He is the Lord our God; throughout all the earth are His judgments.
8 He remembered His covenant forever, the word He had commanded to the thousandth generation,
9 Which He had made with Abraham, and His oath to Isaac,
10 And He set it up to Jacob as a statute, to Israel as an everlasting covenant,
The above verses from Psalm 105 are also found in I Chronicles 16:13-17.

More importantly, that the covenant between G-d and the Jews is eternal is also found immediately following the very passage in question, of 
Jeremiah 31:30-34, beginning with the very next verse:
34 So said the Lord, Who gives the sun to illuminate by day, the laws of the moon and the stars to illuminate at night, Who stirs up the sea and its waves roar, the Lord of Hosts is His name.
35 If these laws depart from before Me, says the Lord, so will the seed of Israel cease being a nation before Me for all time.

So the covenant between G-d and the Jews is an eternal covenant, and when G-d makes a new covenant, it is with the Jews, and it only reaffirms and reestablishes the earlier covenants which G-d had made with the Jews, as we saw regarding Leviticus 26:42 above.

Again, let us look at the first verse of our passage from Jeremiah 31:30-34:
30 Behold, days are coming, says the Lord, and I will form a covenant with the house of Israel and with the house of Judah, a new covenant.
31 Not like the covenant that I formed with their forefathers on the day I took them by the hand to take them out of the land of Egypt, that they broke My covenant, although I was a lord over them, says the Lord.

This is considered a prophecy because of the first words of the verse, “Behold, days are coming, says the Lord.” However, immediately before these few verses that begin with verse 30, there are additional verses that also begin the exact same way, with the words, “Behold, days are coming, says the Lord.” The whole prophecy actually begins with verse 26. As you will read, when one looks at the whole prophecy of Jeremiah 31:26-34, this passage could not have happened yet. Here is the whole passage:

26 Behold days are coming, says the Lord, and I will sow the house of Israel and the house of Judah with seed of man and seed of beasts.
27 And it shall be, as I have watched over them to uproot and to break down, to demolish and to destroy and to afflict, so will I watch over them to build and to plant, says the Lord.
28 In those days, they shall no longer say, "Fathers have eaten unripe grapes, and the teeth of the children shall be set on edge."
29 But each man shall die for his iniquity; whoever eats the unripe grapes- his teeth shall be set on edge
30 Behold, days are coming, says the Lord, and I will form a covenant with the house of Israel and with the house of Judah, a new covenant.
31 Not like the covenant that I formed with their forefathers on the day I took them by the hand to take them out of the land of Egypt, that they broke My covenant, although I was a lord over them, says the Lord.
32 For this is the covenant that I will form with the house of Israel after those days, says the Lord: I will place My law in their midst and I will inscribe it upon their hearts, and I will be their God and they shall be My people
33 And no longer shall one teach his neighbor or [shall] one [teach] his brother, saying, "Know the Lord," for they shall all know Me from their smallest to their greatest, says the Lord, for I will forgive their iniquity and their sin I will no longer remember
34 So said the Lord, Who gives the sun to illuminate by day, the laws of the moon and the stars to illuminate at night, Who stirs up the sea and its waves roar, the Lord of Hosts is His name.

Verse 26 speaks of a time when the House of Israel is reunited with the House of Judah, and when they increase in size as well as in resources.

26 Behold days are coming, says the Lord, and I will sow the house of Israel and the house of Judah with seed of man and seed of beasts. [Jeremiah 31:26]

Then G-d states that just as He watched over the Jews when He saw fit to punish them, so, too, will He continue to watch over the Jews as everything gets better:

27 And it shall be, as I have watched over them to uproot and to break down, to demolish and to destroy and to afflict, so will I watch over them to build and to plant, says the Lord [Jeremiah 31:28]

[Jeremiah 31:28-29]
28 In those days, they shall no longer say, "Fathers have eaten unripe grapes, and the teeth of the children shall be set on edge."
29 But each man shall die for his iniquity; whoever eats the unripe grapes- his teeth shall be set on edge

Jeremiah is saying that when those days come, all will recognize, as the Bible has said repeatedly (See Exodus 32:30-35; Deuteronomy 24:16; and Ezekiel 18:1-4) that the person who sins will always be the only one who gets the punishment for that sin. This is what it states quite simply in Deuteronomy 24:16, No man shall be put to death for the sins of his children, no child will be put to death for the sins of his father. Every man shall be put to death for his own sin.

This description of this messianic age continues with Jeremiah 31:30. The first verse of the passage reads:

30 Behold, days are coming, says the Lord, and I will form a covenant with the house of Israel and with the house of Judah, a new covenant.

However, the House of Israel, which was made up of the Ten Lost Tribes, have been lost and scattered around the world since the fall of the Northern Kingdom around 721 B.C.E.. The House of Israel, the Ten Lost Tribes, cannot be re-united with the House of Jacob, because the House of Israel has not been around for thousands of years, that is why they are called the Ten LOST Tribes. This passage in Jeremiah is describing a Jewish People where all of the descendants of every tribe thrives, and has made their way to the Promised Land. Because it speaks of both the House of Israel and the House of Judah together, with G-d, in a single new covenant.

There is another reference, also in Jeremiah, in the 23rd chapter that describes the same thing, where all the Jews have returned to the Promised Land, and which also begins with the same words found in Jeremiah 31:26 and 31:30

Yirmiyahu - Jeremiah - Chapter 23
5 Behold, days are coming, says the Lord, when I will set up of David a righteous shoot, and he shall reign a king and prosper, and he shall perform judgment and righteousness in the land
6 In his days, Judah shall be saved and Israel shall dwell safely, and this is his name that he shall be called, The Lord is our righteousness.
7 Therefore, behold days are coming, says the Lord, when they shall no longer say, "As the Lord lives, Who brought up the children of Israel from the land of Egypt,"
8 But, "As the Lord lives, Who brought up and Who brought the seed of the house of Israel from the northland and from all the lands where I have driven them, and they shall dwell on their land."

If we look at recent Jewish history we will see that since the Holocaust the Jews have gotten to comfortable in their diaspora. So I believe that's the reason for the rise of antisemitism in Europe, of which is forcing more and more Jews in Europe to make Aliyah to Israel, and this antisemitism is now starting in the United State. 

If we look at prophecy the mashiach can only arrive after all the tribes reunite in Israel. I think the time is near, and we will see the mashiach arrive and as the word mashiach translated means the "anointed one"; he will be anointed King of Israel. 

This leads us, now, to look at the next two verses of our passage:

31 Not like the covenant that I formed with their forefathers on the day I took them by the hand to take them out of the land of Egypt, that they broke My covenant, although I was a lord over them, says the Lord.
32 For this is the covenant that I will form with the house of Israel after those days, says the Lord: I will place My law in their midst and I will inscribe it upon their hearts, and I will be their God and they shall be My people [Jeremiah 31:31-32]

What these verses are saying is that everyone will no longer need to look in any book, neither a 'New Testament,' nor even the Hebrew Scriptures, to tell them what is Right and what is Wrong. They will know it instinctively because it will be in their hearts, truly making G-d their G-d, and in turn, truly making them G-d's People. Certainly this has also not happened yet.

What, precisely, does it mean to have G-d's Torah written in our innermost parts?

I delight to do thy will, O my God: yea, thy Torah is within my heart. [Psalm 40:8]
Because G-d's Torah is within us, we know what we are to do, and we are happy to do it.

Please also read carefully. Jeremiah 31:32 does not say 'I will put my NEW Torah in their inward parts' It says, 'I will inscribe my Torah upon their hearts.' The laws of G-d do not change or get changed, they are eternal as G-d is Eternal:

Devarim - Deuteronomy - Chapter 29
28 The hidden things belong to the Lord, our God, but the revealed things apply to us and to our children forever: that we must fulfill all the words of this Torah.
Tehillim - Psalms - Chapter 19
8 The law of the Lord is perfect, restoring the soul; the testimony of the Lord is faithful, making the simple one wise
9 The orders of the Lord are upright, causing the heart to rejoice; the commandment of the Lord is clear, enlightening the eyes.
10 The fear of the Lord is pure, existing forever; the judgments of the Lord are true, altogether just.

Tehillim - Psalms - Chapter 111
7 The works of His hands are truth and justice; all His commandments are faithful.
8 Steadfast forever, made in truth and uprightness

As a matter of fact, Ezekiel 11:17-20 reflects the ideas found in Jeremiah 31:26-34: that G-d's laws will be in our hearts, not books, in the messianic age, which will last forever:

I delight to do thy will, O my God: yea, thy Torah is within my heart. [Psalm 40:8]
Because G-d's Torah is within us, we know what we are to do, and we are happy to do it.

Please also read carefully. Jeremiah 31:32 does not say 'I will put my NEW Torah in their inward parts' It says, 'I will inscribe my Torah upon their hearts.' The laws of G-d do not change or get changed, they are eternal as G-d is Eternal:

Devarim - Deuteronomy - Chapter 29
28 The hidden things belong to the Lord, our God, but the revealed things apply to us and to our children forever: that we must fulfill all the words of this Torah.

Tehillim - Psalms - Chapter 19
8 The law of the Lord is perfect, restoring the soul; the testimony of the Lord is faithful, making the simple one wise
9 The orders of the Lord are upright, causing the heart to rejoice; the commandment of the Lord is clear, enlightening the eyes.
10 The fear of the Lord is pure, existing forever; the judgments of the Lord are true, altogether just.

Tehillim - Psalms - Chapter 111
7 The works of His hands are truth and justice; all His commandments are faithful.
8 Steadfast forever, made in truth and uprightness

As a matter of fact, Ezekiel 11:17-20 reflects the ideas found in Jeremiah 31:26-34: that G-d's laws will be in our hearts, not books, in the messianic age, which will last forever:

Therefore say, Thus saith the Etrnl G-d; I will even gather you from the people, and assemble you out of the countries where ye have been scattered, and I will give you the land of Israel. And they shall come thither, and they shall take away all the detestable things thereof and all the abominations thereof from thence. And I will give them one heart, and I will put a new spirit within you; and I will take the stony heart out of their flesh, and will give them an heart of flesh: That they may walk in my statutes, and keep mine ordinances, and do them: and they shall be my people, and I will be their G-d. [Ezekiel 11:17-20]

As I wrote above, this new covenant that G-d speaks about in Jeremiah 31 is not talking about a new covenant, a new contract, and He does not mean a new set of laws, a new Torah, a new scripture. It means the covenant between G-d and the Jews and the laws of that covenant are eternal.

Finally, the text from Jeremiah 31 reads,

33 And no longer shall one teach his neighbor or [shall] one [teach] his brother, saying, "Know the Lord," for they shall all know Me from their smallest to their greatest, says the Lord, for I will forgive their iniquity and their sin I will no longer remember [Jeremiah 31:33]