The promise is what we usually call “The New Testament.” Under “The Old Testament” (agreement) true religion consisted of external control and ceremonial laws. The priests alone could come into God’s presence by their rituals and their sacrifices.
Under the New Testament (agreement) Jesus has become your once-for-all sacrifice. As a believer, you are now a priest in whom God the Holy Spirit dwells, and the law of love to God and neighbour inwardly controls your life. Jesus himself is now both your sacrifice and your high priest in heaven.
Jer 31:31-37
The New Agreement with Israel and Judah…
The LORD says, “The time is coming when I will make a new covenant with the people of Israel and with the people of Judah. It will not be like the old covenant that I made with their ancestors when I took them by the hand and led them out of Egypt. Although I was like a husband to them, they did not keep that covenant. The new covenant that I will make with the people of Israel will be this: I will put my law within them and write it on their hearts. I will be their God, and they will be my people. None of them will have to teach a neighbour to know the LORD, because all will know me, from the least to the greatest. I will forgive their sins and I will no longer remember their wrongs. I, the LORD, have spoken.”
The LORD provides the sun for light by day, the moon and the stars to shine at night. He stirs up the sea and makes it roar; his name is the LORD Almighty. He promises that as long as the natural order lasts, so long will Israel be a nation.
If one day the sky could be measured and the foundations of the earth explored, only then would he reject the people of Israel because of all they have done. The LORD has spoken.
