The Hebrews author had explained who Melchizedek was. Now he explains the imperfection of the Levitical priesthood, the change of law that comes from a change of priesthood, and the eternal priesthood of Jesus according to the type of priesthood of Melchizedek.

The New and Living Way | Episode 17 | Hebrews 7:11-19

Now if there was perfection through the Levitical priesthood (for under it hath the people received the law), what further need was there that another priest should arise after the order of Melchizedek, and not be reckoned after the order of Aaron? For the priesthood being changed, there is made of necessity a change also of the law. For he of whom these things are said belongeth to another tribe, from which no man hath given attendance at the altar. For it is evident that our Lord hath sprung out of Judah; as to which tribe Moses spake nothing concerning priests.

And what we say is yet more abundantly evident, if after the likeness of Melchizedek there ariseth another priest, who hath been made, not after the law of a carnal commandment, but after the power of an endless life: for it is witnessed of him, "Thou art a priest for ever after the order of Melchizedek."

For there is a disannulling of a foregoing commandment because of its weakness and unprofitableness (for the law made nothing perfect), and a bringing in thereupon of a better hope, through which we draw nigh unto God.