I'm not aware of any verses that suggest that Israel shall have a human king reigning over them for eternity. The only king of God's kingdom will be Jesus. After all, God never wanted the Israelites to have a human king in the Old Testament days, but they insisted - from 1 Samuel (WEB):Except that David will be raised up to be king over them, yes? I don't see that a valid objection, "But David is dead." It sounds like the argument is, "It doesn't mean David because it can't mean David."
8:5-7
(5) They said to him, “Behold, you are old, and your sons don’t walk in your ways. Now make us a king to judge us like all the nations.”
(6) But the thing displeased Samuel, when they said, “Give us a king to judge us.” Samuel prayed to Yahweh.
(7) Yahweh said to Samuel, “Listen to the voice of the people in all that they tell you; for they have not rejected you, but they have rejected me as the king over them.
10:18-24
(18) and he said to the children of Israel, “Yahweh, the God of Israel, says ‘I brought Israel up out of Egypt, and I delivered you out of the hand of the Egyptians, and out of the hand of all the kingdoms that oppressed you.’
(19) But you have today rejected your God, who himself saves you out of all your calamities and your distresses; and you have said to him, ‘No! Set a king over us.’ Now therefore present yourselves before Yahweh by your tribes, and by your thousands.”
(20) So Samuel brought all the tribes of Israel near, and the tribe of Benjamin was chosen.
(21) He brought the tribe of Benjamin near by their families; and the family of the Matrites was chosen. Then Saul the son of Kish was chosen; but when they looked for him, he could not be found.
(22) Therefore they asked of Yahweh further, “Is there yet a man to come here?” Yahweh answered, “Behold, he has hidden himself among the baggage.”
(23) They ran and got him there. When he stood among the people, he was higher than any of the people from his shoulders and upward.
(24) Samuel said to all the people, “Do you see him whom Yahweh has chosen, that there is no one like him among all the people?” All the people shouted, and said, “Long live the king!”
Wheras eventually, after Jesus turns the kingdom over to God ("When all things have been subjected to him, then the Son will also himself be subjected to him who subjected all things to him, that God may be all in all", 1Cor 15:28), God will be king over all living beings, and he will be with all mankind - Revelation 21:3 (WEB):
(3) I heard a loud voice out of heaven saying, “Behold, God’s dwelling is with people, and he will dwell with them, and they will be his people, and God himself will be with them as their God.
The Cambridge Bible Notes for Hosea 3:5 says:
David their king] There is a great body of authority for regarding this as an expression for the Messiah. So the Targum took it, so Aben Ezra, and other Jewish writers cited by Pococke. The interpretation rests on the undoubted fact that in Jer_30:9; Eze_34:23-24; Eze_37:24-25 ‘David’ means the ideal king of the future who should prove as it were a second David. In all these passages however there is something in the context to determine the reference to a person, and all these passages belong to a later period in the development of the Messianic revelation. The analogy of Amo_9:11 suggests that what is in Hosea’s mind is, not the person of the king, but the dynasty. In short, ‘David’ = the representative of David. Precisely so Rehoboam is still ‘David’ in 1Ki_12:16, and the high priest ‘Aaron’ in Psa_133:2.