'King Over Israel' in the Bible

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

And David knew that the LORD had established him king over Israel; for his kingdom was exalted on high, for his people Israel's sake.

Now David was old and full of days; and he made Solomon his son king over Israel.

However the LORD, the God of Israel, chose me out of all the house of my father to be king over Israel forever. For he has chosen Judah to be prince; and in the house of Judah, the house of my father; and among the sons of my father he took pleasure in me to make me king over all Israel.