The Apostle Paul quotes a somewhat hidden Old Testament passage to show that the priesthood started by this mysterious person made possible Jesus’ role as our heavenly high priest. It is a role that he did not perfectly fulfill until after he was born, suffered, died and was resurrected from the dead (Hebrews 5:7 - 10, 9:11 - 12).
So Christ also did not take upon himself the glory of becoming a high priest. But God said to him, "You are my Son; today I have become your Father. And he says in another place (Psalm 110:4), “You are a priest forever, in the order of Melchizedek” (Hebrews 5:5 - 6, NIV).
God’s law specified that only those born of the tribe of Levi could serve as his priests (Numbers 8). Of these Levites, only those who were descended from Aaron were eligible to become High Priest (Exodus 29:9, 29 - 30, Leviticus 8:12, 16:32). Jesus, however, came from the tribe of Judah, a tribe which Scripture says nothing concerning the priesthood (Hebrews 7:13 - 14). He was not eligible to be a priest. How could he then “legally” serve in such a capacity after his resurrection? The answer is the creation of the order of Melchizedek.
God intended, in advance, that the Old Covenant Levitical priesthood last for only a short time (Hebrews 7:11 - 12, 9 - 10) and be replaced. This is why the Biblical appearance of Melchizedek (Genesis 14:18 - 20) occurred MANY decades before Levi (Abraham’s great-grandson) was born and more than 300 years prior to Israel receiving the law (Exodus 20). The existence of his order, prior to the giving of the law, meant that it would not be bound by its rules regarding the priesthood. This made it possible for Jesus to serve, after his resurrection, as High Priest after the order of Melchizedek.
The Apostle Paul delineates some of the profound ways this order, begun by Melchizedek, is superior to what was instituted under the Old Covenant (Hebrews 7:7). It is a royal or ruling High priesthood (Hebrews 7:1), which is perfect (verse 11), changeless (verse 24) and composed of one individual who always existed (verse 3) and always will (verses 8, 16, 24).
Instead of intercession being accomplished periodically within an earthly temple (see Hebrews 9), it is performed constantly next to God’s throne (Hebrews 7:25 - 26, 8:1 - 2, 10:11 - 12). The covenant that is mediated by the order of Melchizedek is much better (Hebrews 8:6), with better promises, than what was offering under the Old Covenant.