Hebrews 7:11-12 (NASB)
"Now if perfection was through the Levitical priesthood (for on the basis of it the people received the Law), what further need was there for another priest to arise according to the order of Melchizedek, and not be designated according to the order of Aaron? For when the priesthood is changed, of necessity there takes place a change of law also."

Hebrews 7 makes a comparison between the priesthood of Melchizedek and that of Christ. Melchizedek met Abraham when returning from the rescue of Lot. His name, "King of Righteousness," signified him as a type of the Messiah and His Kingdom. The name of his city was "Peace;" and as king of peace he typified Christ, the Prince of Peace, the great Bridge between God and fallen humanity. Nothing is recorded regarding the beginning or end of his life. Thus, he typically resembled the Son of God, whose existence is eternal, who had no one that came before Him, and will have no one come after Him. The Scriptures honor the great King of Righteousness and Peace, our glorious and all-sufficient High Priest and Savior. And the more we examine the beauty of this, the more we will see that the testimony of Jesus is the spirit of prophecy (Revelation 19:10).

This chapter shows that the High Priest who would appear later must be much superior to the Levitical priests. The priesthood and law by which perfection could not come was done away with, not by the blood of animal sacrifices, but by Jesus' own blood. A Priest has risen by whom true believers may be made righteous. That there is a change in law is easy to see. The law that made the Levitical priesthood, showed how weak and mortal the priests of this system were, unable to save their own lives, much less able to save those who came to them. But Jesus, the High Priest of a better and new covenant, holds His office by the power of endless life in Himself; not only to keep Himself alive, but to give spiritual and eternal life to all who rely upon His sacrifice and continual intercession (verses 23-25). The better covenant, of which Jesus was the Guaranty, is not here contrasted with the law of works, by which every transgressor is "under a curse" (Galatians 3:10). It is distinguished from the Old Covenant made with Israel at Mount Sinai. The better New Covenant brings every believer into a clearer, more perfect freedom in Christ, and with more abundant privileges.