en_tn/2ch/21/07.md

the house of David

The word "house" is a metonym for the family that lives in the house. In this case it refers to the kingdom of Judah. See how you translated this in 2 Chronicles 10:19. Alternate translation: "the kingdom of Judah" or "the people of Judah" (See: rc://en/ta/man/jit/figs-metonymy)

he had promised that he would always give life to him and his descendants

"he had promised that David's descendants would always be the ones who ruled Judah." This was the covenant that Yahweh made with David.

always give life to him and his descendants

"always cause him and his descendants to live" or "never destroy him and his descendants"