Secular history tells us that the son of Simon Maccabee, John Hyrcanus I, was both king and priest.
Simon was murdered in 134 BCE by his son-in-law Ptolemy, and was succeeded as high priest and king by his son John Hyrcanus I.
There are no other king/priest combinations recorded in the Bible. In the Scriptures, the man that comes closest to being thought of as both king and priest, is Joshua, the son of Jehozadak, the high priest.
Zechariah 6:9-11:
And the word of the LORD came to me: (10) “Take from the exiles Heldai, Tobijah, and Jedaiah, who have arrived from Babylon, and go the same day to the house of Josiah, the son of Zephaniah. (11) Take from them silver and gold, and make a crown, and set it on the head of Joshua, the son of Jehozadak, the high priest.
But his crowning was obviously done to represent the greater Joshua, known in English as Jesus, as we see in Zechariah 6:12-13:
(12) And say to him, ‘Thus says the LORD of hosts, “Behold, the man whose name is the Branch: for he shall branch out from his place, and he shall build the temple of the LORD. (13) It is he who shall build the temple of the LORD and shall bear royal honor, and shall sit and rule on his throne. And there shall be a priest on his throne, and the counsel of peace shall be between them both.”‘
Notice the reference to “the man whose name is the Branch” in verse 12. This refers to the coming Messiah, as Jeremiah 23:5:
“Behold, the days are coming, declares the LORD, when I will raise up for David a righteous Branch, and he shall reign as king and deal wisely, and shall execute justice and righteousness in the land.
and Jeremiah 33:15 show:
In those days and at that time I will cause a righteous Branch to spring up for David, and he shall execute justice and righteousness in the land.
Imagine how angry the chief priests would have been when Pilate said “Behold the man!” at the trial of Jesus. John 19:5-7:
So Jesus came out, wearing the crown of thorns and the purple robe. Pilate said to them, “Behold the man!” (6) When the chief priests and the officers saw him, they cried out, “Crucify him, crucify him!” Pilate said to them, “Take him yourselves and crucify him, for I find no guilt in him.” (7) The Jews answered him, “We have a law, and according to that law he ought to die because he has made himself the Son of God.”
I’m sure they would have finished that phrase in their minds – Behold the man whose name is the Branch: for he shall branch out from his place, and he shall build the temple of the LORD etc. They would have been so furious it is not surprising they cried out, “Crucify him”.