No, in reading Gen 14:19, we find Melchizedek was just a cohen, priest. High Priest would be worded as Cohen Gadol in Hebrew, and it's not as in Zechariah 3:8.What about Melchizedek? Does he have claims to being a high priest to Abraham?
David and his sons were priests as well, 2 Samuel 8:18.
Psalm 110 speaks of David.