"For the priesthood being changed, there is made of necessity a change also of the law" (Hebrews 7:12).
Did the Levitical priesthood replace the priesthood of Melchizedek?
Under the Old Law of Moses, priests came from the tribe of Levi and, starting with David, kings came from the tribe of Judah. Melchizedek was both a priest and king, which means the authority for his position was not derived from Moses' Law, nor could it have been since Melchizedek lived about 450 years before the law was given.
The writer of Hebrews argued that Jesus is now our High Priest. "Seeing then that we have a great High Priest who has passed through the heavens, Jesus the Son of God, let us hold fast our confession" (Hebrews 4:14). Chapters 5, 6, and 7 in Hebrews are the proof that Jesus is the High Priest. But now the writer points out that since Jesus is the High Priest and he came from the tribe of Judah, then it means the law was changed since members of the tribe of Judah cannot be priests.
"Therefore, if perfection were through the Levitical priesthood (for under it the people received the law), what further need was there that another priest should rise according to the order of Melchizedek, and not be called according to the order of Aaron? For the priesthood being changed, of necessity there is also a change of the law. For He of whom these things are spoken belongs to another tribe, from which no man has officiated at the altar. For it is evident that our Lord arose from Judah, of which tribe Moses spoke nothing concerning priesthood. And it is yet far more evident if, in the likeness of Melchizedek, there arises another priest who has come, not according to the law of a fleshly commandment, but according to the power of an endless life. For He testifies: "You are a priest forever According to the order of Melchizedek"" (Hebrews 7:11-17).
The core of the argument is that there was a prophecy that stated the Messiah would be a priest after the order of Melchizedek; that is, he would be both a priest and king. Jesus was the one this prophecy referred to. Thus, the writer of Hebrews argues that the Old Law was not perfect because otherwise there would not have been a need to search out a priest from a tribe different from Levi. The Law of Moses had to be replaced with a different law and that change was planned by God from long time past.
The Law of Moses with the Levitical priesthood did not replace the order of Melchizedek. Melchizedek was a unique person in history. But it should be noted that someone like Melchizedek could not have existed under the Law of Moses. Jesus' reign is fashioned in the order of Melchizedek's priesthood and kinghood and not in the fashion the Law of Moses required. Therefore, God had changed the law and the prophecy shows that God planned to change the law from long ago.