'King Over Israel' in the Bible

So all the elders of Israel came to the king at 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 through Samuel.

And David realized that the Lord had established him as king over Israel, and that his kingdom was highly exalted, for the sake of His people Israel.

Now when David reached old age, he made his son Solomon king over Israel.

Yet, the Lord, the God of Israel, chose me from all the house of my father to be king over Israel forever. For He has chosen Judah to be a leader; and in the house of Judah, my father’s house, and among the sons of my father He took pleasure in me to make me king over all Israel.