Q: How does Christ execute the office of a priest?
A: Christ executes the office of a priest, in his once offering up of himself a sacrifice to satisfy divine justice, and reconcile us to God; and in making continual intercession for us.
Romans 5:10-11: For if while we were enemies we were reconciled to God by the death of his Son, much more, now that we are reconciled, shall we be saved by his life. More than that, we also rejoice in God through our Lord Jesus Christ, through whom we have now received reconciliation.
It's important, again, to keep the Old Testament understanding of a priest in mind. In the Old Testament, the priests would go before God on behalf of the people. They would offer the sacrifices in the temple. They would intercede for the needs of the people. They acted as liturgists (worship leaders), helping to frame the worship of God's people in a way that God found acceptable. They were the ones who would enter the Holy of Holies on the Day of Atonement. And yet, they themselves were not holy. They themselves were sinful and in need of atonement. The offerings and sacrifices they offered were only temporary. They could not truly restore the people to God. All of it: the priests, the sacrifices, the temple, the liturgy, it all pointed to a Great High Priest, Jesus Christ.
Jesus Christ, who is holy, without blemish, in no need of sanctification, now stands as the head of the people before the throne of God above. He stands there, having lived a life of perfect obedience and righteousness, as the true spotless lamb. He stands there, having offered himself up as the perfect, once for all time sacrifice that is truly able to take away the sins of God's people. He stands there as our minister in the high places, our great liturgist, our worship leader, framing and directing the praises of God's people towards the throne of the Majesty on High in a way that pleases the Father. He has torn the great temple curtain in two, and through him and by him we have been given access to the Holy of Holies. And it is Jesus Christ, the Son of the living God, the visible image of the invisible God, very God of very God, who is interceding for us, praying, as the puritan Thomas Watson said, for our keeping from sin, for our sanctification, and for our glorification. And, he is a great high priest who is able to sympathize with us in every way (Heb. 4:15).
Just as Christ is the prophet, the only prophet we need, he is also the priest. He is the only priest we need. No earthly priest can do what Christ has done and is doing now for us before the throne of God. By no other name do we dare go before the throne of the Father!