A New Covenant is Promised:
(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--
(32) 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.
(33) 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.
(34) 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."
This was yet future to Jeremiah. This had not happened yet. Sins were remembered annually. The Law was not written on their hearts, only on table of stone.
Paul describes this New Covenant:
2 Corinthians 3:1-9
(1) Do we begin again to commend ourselves? Or do we need, as some others, epistles of commendation to you or letters of commendation from you?
(2) You are our epistle written in our hearts, known and read by all men;
(3) clearly you are an epistle of Christ, ministered by us, written not with ink but by the Spirit of the living God, not on tablets of stone but on tablets of flesh, that is, of the heart.
(4) And we have such trust through Christ toward God.
(5) Not that we are sufficient of ourselves to think of anything as being from ourselves, but our sufficiency is from God,
(6) who also made us sufficient as ministers of the new covenant, not of the letter but of the Spirit; for the letter kills, but the Spirit gives life.
(7) But if the ministry of death, written and engraved on stones, was glorious, so that the children of Israel could not look steadily at the face of Moses because of the glory of his countenance, which glory was passing away,
(8) how will the ministry of the Spirit not be more glorious?
(9) For if the ministry of condemnation had glory, the ministry of righteousness exceeds much more in glory.
This New Covenant began only with Jesus' death:
(26) And as they ate, taking the bread and blessing it, Jesus broke and gave to the disciples, and said, Take, eat; this is My body.
(27) And taking the cup, and giving thanks, He gave to them, saying, Drink all of it.
(28) For this is My blood of the New Covenant which concerning many is being poured out for remission of sins.
(1) Now a summary over the things being said: We have such a High Priest, who sat down on the right of the throne of the Majesty in Heaven,
(2) Minister of the Holy of Holies, and of the true tabernacle which the Lord pitched, and not man.
(3) For every high priest is set in place to offer both gifts and sacrifices; from which it is necessary for this One also to have something which He may offer.
(4) For if indeed He were on earth, He would not even be a priest, there being those priests offering gifts according to the Law,
(5) who serve the pattern of and shadow of heavenly things, even as Moses was divinely warned, being about to make the tabernacle: For He says, "See that you make all things according to the pattern being shown to you in the mount."
(6) But now He has gotten a more excellent ministry, also by so much as He is a Mediator of a better covenant, which has been enacted on better promises.
(7) For if that first was faultless, place would not have been sought for a second.
(8) For finding fault, He said to them, "Behold, days are coming, says the Lord, and I will make an end on the house of Israel and on the house of Judah; a new covenant shall be,
(9) not according to the covenant which I made with their fathers in the day of My taking hold of their hand to lead them out of the land of Egypt; because they did not continue in My covenant, and I did not regard them, says the Lord.
(10) Because this is the covenant which I will covenant with the house of Israel after those days, says the Lord, giving My Laws into their mind, and I will write them on their hearts, and I will be their God, and they shall be My people."
(11) "And they shall no more teach each one their neighbor, and each one his brother, saying, Know the Lord; because all shall know Me, from the least of them to their great ones.
(12) For I will be merciful to their unrighteousnesses, and I will not at all remember their sins and their lawless deeds."
(13) In the saying, New, He has made the first old. And the thing being made old and growing aged is near disappearing.
Ezekiel tells us when this New Covenant would come to all of Israel:
(24) For I will take you from among the nations, gather you out of all countries, and bring you into your own land.
(25) Then I will sprinkle clean water on you, and you shall be clean; I will cleanse you from all your filthiness and from all your idols.
(26) I will give you a new heart and put a new spirit within you; I will take the heart of stone out of your flesh and give you a heart of flesh.
(27) I will put My Spirit within you and cause you to walk in My statutes, and you will keep My judgments and do them.
(28) Then you shall dwell in the land that I gave to your fathers; you shall be My people, and I will be your God.
In the Old Covenant, there was the "remembrance of sins", in the New there is not.
(1) For the Law had a shadow of the coming good things, not the image itself of those things. Appearing year by year with the same sacrifices, which they offer continually, they never are able to perfect the ones drawing near.
(2) Otherwise, would they not have ceased to be offered? Because those serving did not still have conscience of sins, having once been cleansed.
(3) But in these there is a remembrance of sins year by year,
(4) for it is not possible for the blood of bulls and goats to take away sins.
Jeremiah 31:34 "For I will forgive their iniquity, and their sin I will remember no more."
In the Old Covenant, the people remained according to their old nature. In the New Covenant, people are remade according to a new nature:
Heb 10:1 For the Law had a shadow of the coming good things, not the image itself of those things. Appearing year by year with the same sacrifices, which they offer continually, they never are able to perfect the ones drawing near.
Heb 10:9-10 then He said, "Lo, I come to do Your will, O God." He takes away the first in order that He may set up the second; by which will we are sanctified through the offering of the body of Jesus Christ once for all.
Hebrews 10:14 For by one offering He has perfected in perpetuity the ones being sanctified.
This New Nature - Regeneration - is simply being "born again":
1 Peter 1:3
(3) Blessed be the God and Father of our Lord Jesus Christ, He according to His great mercy having regenerated us to a living hope through the resurrection of Jesus Christ from the dead,
1 Peter 1:22-23
(22) Having purified your souls in the obedience of the truth through the Spirit to unpretended brotherly love, love one another fervently out of a pure heart,
(23) being regenerated, not by corruptible seed, but incorruptible, through the living Word of God, and remaining forever.
ana - up, genneo - I become . . . upward-born, born again.
John 3:3 Jesus answered and said to him, Truly, truly, I say to you, If one is not generated from above, he is not able to see the kingdom of God.
(5) not by works in righteousness which we had done, but according to His mercy, He saved us through the washing of regeneration and renewal of the Holy Spirit,
From G3825 and G1078; (spiritual) rebirth (the state or the act), that is, (figuratively) spiritual renovation; specifically Messianic restoration: - regeneration.
I like what Thayer says on this one . . .
1) new birth, reproduction, renewal, recreation, regeneration
1a) hence renovation, regeneration, the production of a new life consecrated to God, a radical change of mind for the better. The word often used to denote the restoration of a thing to its pristine state, its renovation, as a renewal or restoration of life after death
I hope this helps . . .
Love in Christ,
ειπεν αυτη ο ιησους εγω ειμι η αναστασις και η ζωη ο πιστευων εις εμε καν αποθανη ζησεται
. . . saying to her Jesus, I AM the resurrection and the life, the one believing into Me even dying shall live . . .