Verse 4 shows us that Jesus is the eternal priest of a new and better covenant. What David writes here stands as the backbone of the book of Hebrews, and two things are extremely important to see.
Firstly, this is a divine oath. This harkens back to the Covenant that God made with David. (See Ps 89:4, 34-35) Yahweh promised that someone from David’s line would sit on his throne forever, and David, back in 2 Samuel 7:16-19, always understood that the fulfillment of the promise to him, to Abraham, and finally to Adam and Eve would be his descendant. All of God’s promises are narrowing on Jesus. He must be the Seed of the Woman, a descendant of Abraham, of the tribe of Judah, and finally, David’s Son.
Secondly, the book of Hebrews makes a huge deal out of the word, “forever” in verse 4. In contrast to the Aaronic Priesthood, where the priests would offer sacrifices over and over and finally die, Christ offers one sacrifice and lives forever. Melchizedek, a biblical person from Genesis 14 is an example of one who according to the book of Hebrews had neither lineage nor end of days (Hebrews 7:3). He stands as a type of Christ, one who was both King of Salem and Priest of God Most High.
At this point, I think we must ask a very probing question. Why - in the middle of a Kingly Psalm - must David insert this stuff about the Messiah being this awesome kind of Priest? David understands by his prophetic role and his own understanding, that all of God’s revelation is pointing to this reality: God’s Kingdom comes by His Covenant, and His Covenant is administered by His Priest. Therefore, the first crown to rest on Christ’s brow would be made of thorns, and His first throne would be a cross. Jesus sits down at the right hand of the Father in verse 1 of Psalm 110 as a sign of a completion of His priestly work. But don’t take my word for it that's exactly the argument of Hebrews 10:12-13. By the completion of His priestly atoning sacrifice, Christ has inaugurated his kingly reign.
We might compare Christ’s priestly atoning work to a chess game. Imagine that you and I are playing chess. (I will have to break the laws of chess a little bit to get this to work, so bear with me) Imagine that in one move, I manage to eliminate all your pieces except for your King while retaining all of my pieces. We could say that this singular move won me the game. This is like Christ’s work on the cross. Satan, sin, and death were utterly defeated in this one moment, but their eternal judgment and Christ’s final checkmate await His return in glory.
I think that this verse has a very natural application into our answer to the question: What is the Gospel? Some voices, even within evangelicalism, have attempted to say that the Gospel is the simple declaration that “Jesus is Lord.” They have foregrounded Christ’s kingly work while neglecting his priestly work. This is a serious error. Ever since the 1st century, men have tried to look away from the bloody hill of Calvary to make the Gospel more palatable. The Romans did not even dare to utter the word, “staurao” or “crucify” since it was considered a dirty word. But Paul had the audacity to write, “But we preach Christ estauromenon” that is “Christ crucified.” (1 Corinthians 1:23)
Therefore, being "gospel-centered" must entail being "cross-centered". At the cross is where our High Priest and King dealt a death blow to the powers of darkness, and his own death could not hold back his exaltation all the way from the grave of Joseph of Arimathea to the place of honor by the Father’s right hand.
We have seen that Christ is qualified to be our King and our Priest, but will he finally rescue us? Will he lay waste to the enemies of God? Will He defeat Satan, death, sin, and all rebels against His throne?