Charles Ellicott Commentary Jeremiah 31:33

"But this is the covenant that I will make with the house of Israel after those days, saith Jehovah: I will put my law in their inward parts, and in their heart will I write it; and I will be their God, and they shall be my people:" — Jeremiah 31:33 (ASV)

This shall be the covenant ... —The prophet felt that nothing less than this would meet the needs of the time, or, indeed, of any time. The experiment, so to speak, of a law requiring righteousness had been tried and had failed.

There remained the hope—now, by the divine word that came to him, turned into an assurance—of a Power imparting righteousness, writing the law in the inward parts, the centre of consciousness and will, in which God required truth (Psalms 2:6), in the heart as the region of both thoughts and affections. In 2 Corinthians 3:3–6 we have a clear reference not only to the idea, but to the very words of Jeremiah’s prophecy.