When I first heard of the New Covenant I thought it just consisted of 1) Regeneration (law written on the “heart” (Jer. 31: 33)) and 2) Justification (forgiveness of sins (Jer. 31.34)) as expounded in Jeremiah 31:31-34:
31"Behold, the days are coming, declares the LORD, when I will make a new covenant with the house of Israel and the house of Judah, 32not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt, my covenant that they broke, though I was their husband, declares the LORD. 33But this is the covenant that I will make with the house of Israel after those days, declares the LORD: I will put my law within them, and I will write it on their hearts (REGENERATION). And I will be their God, and they shall be my people. 34And no longer shall each one teach his neighbor and each his brother, saying, 'Know the LORD,' for they shall all know me, from the least of them to the greatest, declares the LORD. For I will forgive their iniquity, and I will remember their sin no more(JUSTIFICATION)".
The Return from Exile and The Restoration of Israel and Judah
But as I examine the surrounding context of Jer. 31:31-34, it seems that the “regeneration” and “justification” elements are situated in the “Return from Exile” (Jer. 30:3, 10,18, 31:6,8-9.10,16-17,21, and 32:37) and the “Restoration of Israel and Judah” (Jer. 30:3.7,10,11,17-20,22,31:1,4,38,40 and 33:6-9,11, 14) motifs.
An example of the“regeneration” element being found in the context of the “Return from Exile” and the “Restoration of Israel and Judah” motifs can be found in Jeremiah 32:37-41:
“37Behold, I will gather them from all the countries to which I drove them in my anger and my wrath and in great indignation. I will bring them back to this place (RETURN FROM EXILE), and I will make them dwell in safety. 38And they shall be my people, and I will be their God. 39I will give them one heart and one way, that they may fear me forever (REGENERATION) , for their own good and the good of their children after them. 40I will make with them an everlasting covenant, that I will not turn away from doing good to them. And I will put the fear of me in their hearts, that they may not turn from me. 41I will rejoice in doing them good, and I will plant them in this land in faithfulness, with all my heart and all my soul (RESTORATION).”
Also an example of the "justification" element being situated in the “Restoration of Israel and Judah” motif can be found in Jeremiah 33:6-9:
6Behold, I will bring to it health and healing, and I will heal them and reveal to them abundance of prosperity and security. 7I will restore the fortunes of Judah and the fortunes of Israel, and rebuild them as they were at first (RESTORATION). 8I will cleanse them from all the guilt of their sin against me, and I will forgive all the guilt of their sin and rebellion against me. (JUSTIFICATION) 9And this city[c] shall be to me a name of joy, a praise and a glory before all the nations of the earth who shall hear of all the good that I do for them. They shall fear and tremble because of all the good and all the prosperity I provide for it (RESTORATION).
So maybe when the Jews of Jesus’ and Paul’s day heard the term “new covenant” (Luke 22:20, 1 Corinthians 11:25), they thought of “regeneration” and “justification” in the context of Return from Exile” and “Restoration of Israel and Judah” motifs