The New Testament book that speaks the most about Christ as Priest is Hebrews.
The Old Testament backbone of Hebrews consists of two verses quoted from Psalm 110. Verse 1 is cited to confirm that Christ is exalted above all because He sat down at the right hand of God. This is a recurring theme in Hebrews, one that emphasizes Jesus’ divinity and Messiahship (Heb. 1:3, 4:14, 7:26, 8:1, 12:2). Psalm 110:4 is used to demonstrate that Christ’s priesthood has been foreshadowed by Melchizedek (Heb. 5:6).
The Bible does not provide much information regarding Melchizedek. Yet, what it does reveal shows remarkable similarities to Jesus. Melchizedek is the king of the city Salem (Salem means “peace,” so he is the “King of Peace”). His name means “King of Righteousness,” which speaks of his character. He is detached from history, as his familial line is not given; his birth and death are not mentioned; so, it seems as if he had no beginning and no end; and he is “priest of the Most High God.” Melchizedek’s priesthood is superior to the Levitical priesthood, because through Abraham, Levi gave tithes to Melchizedek (Heb. 7:4–10). Melchizedek, then, is a type of Christ.
But Christ is even more. Aaron was the first high priest in Israel. Hebrews 5:1–4 describes an idealized Aaronic high priestly office: divine appointment, representative of men, mediation before God, compassionate, and offering sacrifices for the people and for himself.
The book of Hebrews portrays Christ as the new High Priest. He is of a better order than even Aaron; not only does He fulfill the requirements of the Aaronite priesthood, He enhances them. Jesus had no sin, was fully obedient, and did not need to bring an offering for Himself. On the contrary, He Himself was the offering–the most perfect offering possible.
Jesus fulfilled both the Aaronite and the Melchizedek high priesthood in a better way than either of those priests, or priesthoods, ever did or could. Both types met their antitype in Christ.