Let us go to verse 4. Verse 4 is a new section. This is a new oracle, and it switches gears. "The Lord has sworn and will not relent, 'You are a priest forever according to the order of Melchizedek.'" Now this is speaking of Messiah, not as king, not as powerful ruler who bashes his enemies on their heads. This is calling Messiah as a priest, showing Him as a priest. And the author of Hebrews uses this verse extensively from Hebrews 5 to Hebrews 10, six chapters there, and he expands on just this point extensively. You want a college level course on Psalm 110:4? Read Hebrews because this is what he is talking about. Why does Jesus Christ qualify as the High Priest when He is not a Levite, He is not from Aaron? How can that be? And he goes through step-by-step-by-step-by-step showing how He qualified to be a priest after the order of Melchizedek.
Now, what we see here in Psalm 110:4 is that the Father swears an oath—the highest of all oaths—and it says it is an irrevocable vow. He will not change His mind once it is said. It is sure because He will make sure it is coming to pass that His Son—the One that is called the Word, the King—is also the eternal and undying High Priest. He will fill both offices. He qualified for both offices. Whereas men had to have one as king and another man as a priest, He fulfills both and He fulfills both perfectly.
And as Hebrews 7 explains, this order—the order of Melchizedek—supersedes the Levitical priesthood. And he proves it by saying Abraham paid tithes to Melchizedek. And he says Levi was still in the loins of Abraham when he did this. And the lesser always pays tithes to the greater. So he said, "Hey, if Abraham paid tithes to Melchizedek and Levi was not even around, then this shows that the order of Melchizedek is a higher body of priests, order of priests, than the Levitical priesthood." By the way, as he also explains in Hebrews 7, Melchizedek means King of righteousness, and since he ruled from Salem, he is also King of peace, and those obviously both fit Jesus Christ.
Now, there is one more highly significant part of this psalm, which is verse 4:
At first glance, this reference to a Priest may seem out of place because everything else has been about kingship after Christ’s enthronement. But this psalm foretells that David’s Lord would also be a Priest—the ultimate Priest. This was not possible in Israel, where the kings descended from David, who was of the tribe of Judah, and the priestly line was of the tribe of Levi, and more specifically, of the house of Aaron. But the One sitting down would also be a Priest. The two roles would be combined in the Messiah.