How is the Lord Jesus Christ a priest like Melchisedec?

What is the significance of "Thou art a priest for ever after the order of Melchisedec" (Psalm 110:4)?

Aaronic priests served in an earthly sanctuary with repeated sacrifices under an old covenant. By comparison and contrast, Christ’s priesthood is linked with a heavenly sanctuary, a final sacrifice, and an eternal covenant (Hebrews 7-10). Israel’s high priest transferred his office to his son. Our Great High Priest (4:14) is unique. Melchisedec, like the Son of God, did not derive His office from ancestors nor delivered it to successors, since his genealogy and posterity are not recorded (Genesis 14:18; Hebrews 7:3). The Bible’s first priest, Melchisedec, is from a mold into which no one else fits. The original (the mold), in God’s purpose, is His Son.

Melchisedec was both a priest and king. The meaning of his name and title, King of Righteousness, King of Peace (7:2) is significant (Psalm 72:3; Isaiah 60:17). He appears after the Bible’s first war and battle, involving a confederacy of kings (Genesis 14; Psalm 2:2). He assures Abram of God’s ability to give him the land of promise. All of this reminds us of a coming day when our Lord will be a priest on His throne (Zechariah 6:13). Until then, we enjoy the benefit of His priesthood.

The single, defining act of Melchisedec’s priesthood was blessing Abram (Hebrews 7:1). By lifting Abram’s vision to "the most high God, possessor of heaven and earth," he strengthened the pilgrim’s faith to withstand the coming trial.

Assured by an oath of the immutable God (Hebrews 7:21), our Lord’s priesthood "after the order of Melchisedec" is non-transferable, eternal, millennial, and spiritual, strengthening faith in the Unseen.

D. Oliver