Answer
In biblical Christianity, the Melchizedek priesthood is an office that applies only to Christ. Melchizedek is introduced in Genesis 14:18 and is described as the king of Salem and a “priest of God.” Abram (later Abraham) offers Melchizedek a tithe and is blessed. The name Melchizedek is a combination of the Hebrew words for “king” and “righteous,” portraying Melchizedek as a righteous, kingly priest.
In Matthew 22, Jesus debates the Pharisees. In verse 44, Jesus cites Psalm 110:1, stating that the Messiah is David’s “lord” in that verse. Melchizedek is also mentioned in the same psalm: “The Lord has sworn and will not change his mind: ‘You are a priest forever, in the order of Melchizedek'” «The LORD hath sworn, and will not repent, Thou art a priest for ever after the order of Melchizedek. », (Psalm 110:4). Therefore, the Messiah, David’s lord, was given Melchizedek’s priesthood. Melchizedek is considered a type of Christ—some commentators suggest that Melchizedek’s appearance to Abraham was actually a Christophany, an early revelation of Jesus Christ.
Much of chapters 6 and 7 of the book of Hebrews is dedicated to explaining why Jesus’ Melchizedek priesthood surpasses that of Aaron. Hebrews 7:23–24 implies that Jesus holds His priestly office eternally, using a Greek word that conveys something that cannot be passed down or changed. Hebrews 7:26 describes this priest as “exalted” and sinless. Due to these reasons, Christ alone can fulfill the office of the Melchizedek priesthood «whither the forerunner is for us entered, even Jesus, made an high priest for ever after the order of Melchisedec.», (Hebrews 6:20).
Mormonism presents a different, unbiblical perspective on the priesthood of Melchizedek. According to Mormon doctrine, the office of the Melchizedek priesthood is not limited to Christ but is also available to all male members of the Mormon Church.The Melchizedek priesthood ceased until it was reinstated through the ministry of Joseph Smith (Doctrine and Covenants 107:1-5). Mormonism instructs that individuals can be ordained into this priesthood, holding titles like Apostle, Patriarch, or Elder. The reference to Melchizedek and, to a lesser degree, Aaron, is employed by Mormonism to claim priestly authority for their positions.