In brief, this chapter argues that the priesthood of Levi is inferior to the priesthood of Melchizedek. This is because Levi is less than his ancestor Abraham who is less than Melchizedek to whom Abraham gave tithes.
4, 7 Now consider how great this man was, to whom even the patriarch Abraham gave a tenth of the spoils. Now beyond all contradiction the lesser is blessed by the better.
9, 10 Even Levi, who receives tithes, paid tithes through Abraham, so to speak, for he was still in the loins of his father when Melchizedek met him.
Jesus who was of the tribe of Judah and not of Levi thus did not belong to the Levitical priesthood. Instead he belonged to the priesthood of Melchizedek because Jesus, like Melchizedek, is “without father, without mother, without genealogy, having neither beginning of days nor end of life, but made like the Son of God, remains a priest continually.” (v3)
Thus, the New Testament is again shown to be superior to the Old Testament that it replaces because of the superiority of its priesthood. The Levitical priests were mortal (v23) but Jesus is immortal!
24-25 But He, because He continues forever, has an unchangeable priesthood. Therefore He is also able to save to the uttermost those who come to God through Him, since He always lives to make intercession for them.
The King of Righteousness is He and so he hears our every cry for justice and forgives our every repentant plea for mercy. The King of Peace (Salem, v2) is He and so He bridges the separation between God and us, making peace in His body which was sacrificed for us (Ephesians 2:14-16).
Peace I leave with you, My peace I give to you; not as the world gives do I give to you. Let not your heart be troubled, neither let it be afraid.