Q: How doth Christ execute the office of a priest?
A: Christ executeth 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.

Hebrews 9:14, 28. How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God? ...So Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation.
Romans 3:26. To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus.
Hebrews 2:17. Wherefore in all things it behoved him to be made like unto his brethren, that he might be a merciful and faithful high priest in things pertaining to God, to make reconciliation for the sins of the people.
Hebrews 7:25. Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.

Westminster Project - Francis Beattie on the Priestly and Kingly Role of the Mediator