In Israel the kingship and priesthood were completely separate. The priests were from the tribe of Levi, and the kings were from the tribe of Judah.
فَقَدْ تَحَدَّرَ ٱلْكَهَنَةُ مِنْ سِبْطِ لَاوِي ،‏ أَمَّا ٱلْمُلُوكُ فَمِنْ سِبْطِ يَهُوذَا .‏