Nathan refers to David in the third person. This is a way of showing respect to the king. It can be stated in second person. Alternate translation: "Have you, my master the king, done this without telling us, your servants, who should sit on the throne after you?" (See: [[rc://en/ta/man/jit/figs-123person]])
Sitting on the throne is a metonym for being king. See how you translated similar words in [1 Kings 1:13](../01/13.md). Alternate translation: "who would be king after him" (See: [[rc://en/ta/man/jit/figs-metonymy]])