Hebrews 7:11-17

¹¹ So 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? ¹² For when the priesthood is changed, of necessity there takes place a change of law also. ¹³ For the one about whom these things are said belongs to another tribe, from which no one has officiated at the altar. ¹⁴ For it is evident that our Lord was descended from Judah, a tribe with reference to which Moses said nothing concerning priests. ¹⁵ And this is clearer still, if another priest arises according to the likeness of Melchizedek, ¹⁶ who has become a priest not on the basis of a law of physical requirement, but according to the power of an indestructible life. ¹⁷ For it is attested of Him,

“You are a priest forever
According to the order of Melchizedek.”

What further need?: If the old way worked, then why do we have a new way? The Old Covenant, therefore, was ineffective at bringing about salvation. This is why a New Covenant was needed.

For when the priesthood is change: When the priesthood is changed, as in the case of Melchizedek, then the covenant must change. This means that Jesus, being a High Priest outside of the Old Covenant, has initiated a better covenant. This is why the author says that the Lord Jesus was descended from Judah, a tribe with reference to which Moses said nothing concerning priests. Jesus has arisen, therefore, as a High Priest outside of the law and consequently in the line of Melchizedek who was also outside of the law.