Heb 8:13 In that He says, "A new covenant," He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away.
Jeremiah prophesied the New Covenant which would made their existing covenant then, based on the Law of Moses (Judaism) obsolete. This will mean that those in the new covenant must not follow the old covenant which had become obsolete and unacceptable to God.
What is this New Covenant?
Jer 31:31 "Behold, the days are coming, says the Lord, when I will make a new covenant with the house of Israel and with the house of Judah— not according to the covenant that I made with their fathers in the day that I took them by the hand to lead them out of the land of Egypt, My covenant which they broke, though I was a husband to them, says the Lord. But this is the covenant that I will make with the house of Israel after those days, says the Lord: I will put My law in their minds, and write it on their hearts; and I will be their God, and they shall be My people. No more shall every man teach his neighbor, and every man his brother, saying, 'Know the Lord,' for they all shall know Me, from the least of them to the greatest of them, says the Lord. For I will forgive their iniquity, and their sin I will remember no more."
In the New Covenant, God lays down the following conditions:-
1. I will put My law in their minds
2. I will write it on their hearts;
3. They shall be My people, and I will be their God.
4. No more shall every man teach his neighbor... they all shall know Me, from the least of them to the greatest of them,
5. For I will forgive their iniquity, and their sin I will remember no more."*
6. I will put a new spirit within them,
7. They may walk in My statutes
8. keep My judgments and do them
Jer 11:19-20 Then I will give them one heart, and I will put a new spirit within them, and take the stony heart out of their flesh, and give them a heart of flesh, that they may walk in My statutes and keep My judgments and do them; and they shall be My people, and I will be their God.
Fulfillment of the New Covenant
Luke 24:46 Then He said to them, "Thus it is written, and thus it was necessary for the Christ to suffer and to rise from the dead the third day, and that repentance and remission of sins should be preached in His name to all nations, beginning at Jerusalem."
Once a Jew (Peter, Paul, John (or anyone else) has accepted the gospel of Jesus, he is a born again Christian. He must immediately discard all his former belief and practices of Judaism found in the OT (or other religions) and obey the commandments of our Lord Jesus and the Epistles of His Apostles for:-
1. All his sins are cleansed by the blood of Jesus
2. He is sealed with the Holy Spirit
3. He becomes a child (people) of God.
4. The Spirit of truth will guide, lead and teach him all truth.
John 14:15-17a, 26; 16:13 "If you love Me, keep My commandments. And I will pray the Father, and He will give you another Helper, that He may abide with you forever— the Spirit of truth... But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things that I said to you... However, when He, the Spirit of truth, has come, He will guide you into all truth; for He will not speak on His own authority, but whatever He hears He will speak; and He will tell you things to come.
The New Covenant prophesied by Jeremiah is the Grace of God in Christ Jesus.