en_obs-tn/content/21/05.md

would not be like

The New Covenant would be truly effective. People really would know God, they would truly live as his people, and He would forgive their sins completely, based on the Messiah’s sacrifice of himself one time for all who believe in him.

writing his law on their hearts

This is a metaphor meaning, “help his people to understand his laws and to earnestly desire to obey them.” If possible, keep the image of writing on their hearts, since this is in contrast with the way God had written his law on stone tablets for the Israelites. If that is not possible, you could just translate the meaning.

be his people

This could be translated as, “be his special people” or, “be his favored people.”