In a very literal sense it is neither the offering nor the priest. In a metaphoric sense, both did.
In the sacrificial system we have two elements: (a) the animal, eg, the lamb, and, (b) the priest. BOTH represented Christ but the shadow could not remove sin.
A. The sacrificial system could not remove sin and had no salvific value
- Heb 8:5 - The place where they [the priests] serve is a copy and shadow of what is in heaven.
- Heb 9:9 - It [the sanctuary] is an illustration for the present time, because the gifts and sacrifices being offered were unable to cleanse the conscience of the worshiper.
- Heb 10:4 - because it is impossible for the blood of bulls and goats to take away sins.
- Ps 51:16, 17 - For You do not delight in sacrifice, or I would bring it; You take no pleasure in burnt offerings. The sacrifices of God are a broken spirit; a broken and a contrite heart, O God, You will not despise.
- 1 Sam 15:22 - But Samuel declared: “Does the LORD delight in burnt offerings and sacrifices as much as in obedience to His voice? Behold, obedience is better than sacrifice, and attentiveness is better than the fat of rams.
See also Heb 9:8, 9, 11-14, 10:1, Col 2:16, 17, Isa 1:10-17, Ps 40:6-8, 51:16, 17, 1 Sam 15:22, Hos 6:6, Prov 15:8, 21:3, Jer 6:20, Micah 6:6-8, etc
B. The sacrificial animals (lambs, etc) only represented Jesus who removes sin
- John 1:29 - The next day John saw Jesus coming toward him and said, “Look, the Lamb of God, who takes away the sin of the world!
- 1 Cor 5:7 - For Christ, our Passover lamb, has been sacrificed.
- 1 Peter 1:19 - but with the precious blood of Christ, a lamb without blemish or spot.
C. The Priests were a metaphor of Jesus ministry as Priest
- Heb 4:14, 15 - Therefore, since we have a great high priest who has passed through the heavens, Jesus the Son of God, let us hold firmly to what we profess. For we do not have a high priest who is unable to sympathize with our weaknesses, but we have one who was tempted in every way that we are, yet was without sin.
- Heb 7:23-28 - Such a high priest [Jesus] truly befits us—One who is holy, innocent, undefiled, set apart from sinners, and exalted above the heavens. Unlike the other high priests, He does not need to offer daily sacrifices, first for His own sins and then for the sins of the people; He sacrificed for sin once for all when He offered up Himself. For the law appoints as high priests men who are weak; but the oath, which came after the law, appointed the Son, who has been made perfect forever.
Thus, the OT ceremonial/Levitical system was only a shadow of the realities (Col 2:17, Heb 8:5, 10:1). That is, neither the OT priest nor the sacrifice could take away sin - that is done in Christ alone.
Acts 4:12 - Salvation exists in no one else, for there is no other
name under heaven given to men by which we must be saved.”