The Messiah would be both a High Priest and a King.
OT Prophecy NT Fulfillment
Zechariah 6:12-13
"[12] And speak unto him, saying, Thus speaketh the Lord of hosts, saying, Behold the man whose name is The BRANCH; and he shall grow up out of his place, and he shall build the temple of the Lord: [13] Even he shall build the temple of the Lord; and he shall bear the glory, and shall sit and rule upon his throne; and he shall be a priest upon his throne: and the counsel of peace shall be between them both."
Hebrews 8:1
"Now of the things which we have spoken this is the sum: We have such an high priest, who is set on the right hand of the throne of the Majesty in the heavens;"
Romans 8:34
"Who is he that condemneth?  It is Christ that died, yea rather, that is risen again, who is even at the right hand of God, who also maketh intercession for us."

Tanakh - Neviim - Zechariah 6:12-13

"[12] and speak unto him, saying: Thus speaketh HaShem of hosts, saying: Behold, a man whose name is the Shoot, and who shall shoot up out of his place, and build the temple of HaShem; [13] even he shall build the temple of HaShem; and he shall bear the glory, and shall sit and rule upon his throne; and there shall be a priest before his throne; and the counsel of peace shall be between them both."

Hebrew OT - Zechariah 6:12-13

חמצ שיא-הנה רמאל תואבצ הוהי רמא הכ רמאל וילא תרמאו    [12]   
.הוהי לכיה-תא הנבו חמצי ויתחתמו ומש          
ואסכ-לע לשמו בשיו דוה אשי-אוהו הוהי לכיה-תא הנבי אוהו  
 [13]   
.םהינש ןיב היהת םולש תצעו ואסכ-לע ןהכ היהו          

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