'King Over Israel' in the Bible

So all the elders of Israel came to the king at Hebron, and David made a covenant (solemn agreement) with them there before the Lord; and they anointed him king over Israel, in accordance with the word of the Lord through Samuel.

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

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

However, the Lord, the God of Israel, chose me from all in my father’s house to be king over Israel forever. For He has chosen Judah to be the leader; and in the house (tribe) of Judah he chose the house of my father; and among the sons of my father He was pleased to make me king over all Israel.