en_tn/jer/31/33.md

the house of Israel

The word "house" is a metonym for the family that lives in the house. In this case it refers to the kingdom of Israel. See how you translated this in Jeremiah 3:18. Alternate translation: "Israel" or "the kingdom of Israel" or "the people of Israel" (See: rc://en/ta/man/translate/figs-metonymy)

this is Yahweh's declaration

Yahweh speaks of himself by name to express the certainty of what he is declaring. See how you translated this in Jeremiah 1:8. Alternate translation: "this is what Yahweh has declared" or "this is what I, Yahweh, have declared" (See: rc://en/ta/man/translate/figs-123person)

I will place my law within them and will write it on their heart

These two phrases have similar meanings and emphasize that Yahweh's law will become a part of them, rather than merely written on stone. Here "heart" represents "emotions" or "mind." Alternate translation: "My law will be part of their thoughts and emotions" (See: rc://en/ta/man/translate/figs-parallelism and rc://en/ta/man/translate/figs-metonymy)