Psalm 110:4 (ESV)
4 The LORD has sworn and will not change his mind, “You are a priest forever after the order of Melchizedek.”
David, as the poet of Psalm 110, has been searching for a future in which the monarchy enters into a combination with the priesthood, as was the case in the old days of Salem with Melchizedek. In Israel’s history, the offices of king and priest are always divorced from each other. David expresses the expectation that at one time the king will also be an eternal priest at God’s right hand. The combination of the royal and priestly office is prophesied by Zechariah 6:13. This appeal to the name of Melchizedek in Psalm 110:4 empowers Jesus’ priesthood as being distinct from and superior to the Levitical priesthood.1
6 as he says also in another place, “You are a priest forever, after the order of Melchizedek.”