If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron? For the priesthood being changed, there is made of necessity a change also of the law. Hebrews 7:11-12

The book of Hebrews give a great explanation of the fulfillment of the Old Covenant and the birth of the New Covenant. As the author explains here, since Jesus is now our eternal High Priest, the law must change. The Levitic priesthood was part of the Old Covenant and necessary for people to have a mediator between them and God

However now that Christ, being our Lamb of God, has reconciled us back to the Father. Jesus is our mediator with God, Jesus is our eternal High Priest, Jesus fulfilled The Law. 

For he of whom these things are spoken pertaineth to another tribe, of which no man gave attendance at the altar. For it is evident that our Lord sprang out of Juda; of which tribe Moses spake nothing concerning priesthood.  Hebrews 7:13-14

The Messiah or Christ was to rule from Judah, which Jesus fulfilled. Christ is the Lion of Judah, however no priest were ever prophesied from the line of David. The Levitical line of priests was another foreshadow of Christ to come. This has now been fulfilled and Jesus is our eternal High Priest

And it is yet far more evident: for that after the similitude of Melchisedec there ariseth another priest, Who is made, not after the law of a carnal commandment, but after the power of an endless life For he testifieth, Thou art a priest for ever after the order of Melchisedec. Hebrews 7:15-17

Jesus the eternal High Priest, was not from The Law, but from the power of the Resurrection. For the Law brings death, but Grace brings eternal life. Just as Melchizedek was an eternal figure, he was a foreshadow of the eternal High Priest who is Jesus

For there is verily a disannulling of the commandment going before for the weakness and unprofitableness thereof. For the law made nothing perfect, but the bringing in of a better hope did; by the which we draw nigh unto God. And inasmuch as not without an oath he was made priest: Hebrews 7:18-20

For The Law made nothing perfect, The Law actually brings death. However Christ made us righteous before the Father. Therefor because Jesus fulfilled The Law, he is now our High Priest. Now because of Christ, we can now draw near to God, because our sins have been atoned for

(For those priests were made without an oath; but this with an oath by him that said unto him, The Lord sware and will not repent, Thou art a priest for ever after the order of Melchisedec:)by so much more Jesus has become a surety of a better covenant. Hebrews 7:21-22

Jesus has made a better covenant, a better testament, because He has fulfilled The Old Covenant. Jesus is our Lamb of God, Jesus is our High Priest, Jesus is our Lord and Savior Amen!