A most interesting sermon by O. Palmer Robertson on Hebrews 7. He covered verses 1-15 and I wish he had finished the entire chapter. He stated that Heb 7 is actually an exposition on Psa 110:4 and so the outline followed the verse in Psalms. One of the more interesting parts was that on The Oath of God. Jesus, after the Order of Melchezedek, an an Covenantal Oath applied, namely "a priest forever" and that secured Christ as our priest for all eternity. The Lord God has pronounced a Oath on David securing the throne to his children but never pronounced such an Oath on Aaronic/Levitical Priesthood. So the Levitical passes away with all the sacrifices and ceremonies while Christ establishes the new Covenant in His blood and with it the new priesthood, after the Order of Melchezedek.
A second note was that Melchezedek was a Gentile priest and hence a priest for all the Nations. This is a fulfillment of Christ as the Savior and Light for all the nations.