What does Hebrews 7:11 mean?
This verse begins a second point, building on the conclusions from verses 1 through 10. The purpose of these next verses is to use God's own Word to show that He intended the priesthood of Melchizedek, not the priesthood of Aaron, to be mankind's ultimate salvation. The use of the term perfection here is mostly meant in the sense of completion. This will be better explained in upcoming Scriptures.The main argument used here is that of God's promise to establish a priesthood in the order of Melchizedek. If the Aaronic priesthood was perfect, why would God want to use something different? Logically, then, we are to assume that God's plan was to use the Melchizedek priesthood, not the Aaronic priesthood, as His perfect means of salvation. This is supported, later, by once again mentioning Psalm 110:4, a verse already cited in the book of Hebrews (Hebrews 5:6; 6:20). There, long after the establishment of the Aaronic priesthood, God promises to establish "forever" a Promised One in the priestly order of Melchizedek (Hebrews 7:17).
The following verses will point out that the promises connected to Messiah require a priest, but also require one who is part of the tribe of Judah, not Levi. This, in turn, will be connected to Melchizedek's symbolic lack of genealogy in the Old Testament: the priesthood of Jesus is endless and superior to that of the Levitical order (Romans 6:14).