'King Over Israel' in the Bible

So all the elders of Israel came to the king to Hebron; and king David made a covenant with them in Hebron before the LORD: and they anointed David king over Israel.

And David perceived that the LORD had established him king over Israel, and that he had exalted his kingdom for his people Israel's sake.

But when the Philistines heard that they had anointed David king over Israel, all the Philistines came up to seek David; and David heard of it, and went down to the stronghold.

And Nathan said to David, You are the man. Thus says the LORD God of Israel, I anointed you king over Israel, and I delivered you out of the hand of Saul;

And David said, What have I to do with you, you sons of Zeruiah, that you should this day be adversaries unto me? shall there any man be put to death this day in Israel? for do not I know that I am this day king over Israel?