Sitting on the "throne of David" is a metonym for having the right to rule; only David's descendants could be king over Israel. Alternate translation: "has the right to rule as David's descendant" (See: [[rc://en/ta/man/translate/figs-metonymy]])
This can be translated as a new sentence. Alternate translation: "his kingdom. He will establish and protect his kingdom, and he will do what is fair and just"