Hebrews 6:13-20 (ESV)
For when God made a promise to Abraham, since he had no one greater by whom to swear, he swore by himself,  saying, "Surely I will bless you and multiply you."  And thus Abraham, having patiently waited, obtained the promise.  For people swear by something greater than themselves, and in all their disputes an oath is final for confirmation.  So when God desired to show more convincingly to the heirs of the promise the unchangeable character of his purpose, he guaranteed it with an oath,  so that by two unchangeable things, in which it is impossible for God to lie, we who have fled for refuge might have strong encouragement to hold fast to the hope set before us.  We have this as a sure and steadfast anchor of the soul, a hope that enters into the inner place behind the curtain,  where Jesus has gone as a forerunner on our behalf, having become a high priest forever after the order of Melchizedek.
“A hope that enters into the inner place behind the curtain where Jesus has gone as a forerunner on our behalf, having become a high priest forever after the order of Melchizedek.” Melchizedek is an enigma in the Old Testament. We know he was a priest of the Most high God and he resided in Jerusalem. It seems others aside from Abraham still knew the Most High God, the True God. It is strange that so many other religions would be there. In the Old Testament, it is shown again and again, that even pagan priest knew the true God, and feared him, though maybe not quite as much as they should have. Abraham offered a tithe to Melechizedek, when he defeated the four kings in battle.
In any case, that Jesus is our High Priest according to this order, as he was not a Levite, and therefore could not hold the Aaronic Priesthood, should be a source of great comfort to us. In Mormon Land you really can’t read this passage without all sorts of thoughts hitting your head, concerning their “priesthoods.”
These two priest hoods never existed side by side. Aaron was given the priesthood through Moses, at this all sacrifices had to be offered through the sons of Aaron. Before this you find that people offered sacrifices to God wherever and whenever they pleased. We don’t know what the regulations were for these sacrifices, though there do seem to be some. For instance Noah was commanded to take clean animals on the ark, long before clean and unclean was spelled out in Leviticus. In any case with Moses, it is no longer permissible for people to offer sacrifices as Job did. This is forbidden, there is one priesthood, and they offer sacrifices, they and they alone. And they do so in only one place, the tabernacle, where God has made His Name known. If God made his Name known in another place, then the Tabernacle, and the Ark of the Covenant moved there. No longer was there room for another order of priests.
But when Jesus offers the final perfect sacrifice of his body, he also does away with the need for the Aaronic Priesthood. He becomes our high priest, and enters behind the curtain, there he intercedes for the church. No longer are sacrifices needed, so the purpose of the Aaronic priesthood are done away with. To be sure there was a time of transition in which the Aaronic Priesthood still operated in the temple, and even the Apostles would go to the temple. But the apostles also knew that these sacrifices were no longer needed, and the day of the temple was soon passing, for the Temple had been replaced with the Body of Christ.