Hebrews 7:11-19 meaning

The Pauline Author points out that if the system of the Levitical priesthood (the law) made the people perfect, there would have been no need for a priest to be appointed outside of the Levitical priesthood. The Pauline Author points out that the people received the Law on the basis of the Levitical priesthood. 

And because the Levite priests did not bring perfection, then neither did the law. Now if perfection was through the Levitical priesthood…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 (v 11)?

The Pauline Author writes that on the basis of the Levitical priesthood the people received the law (v 11). The priests were an integral part of the law. In Numbers 18:5, God said to the Levites, "So you shall attend to the obligations of the sanctuary and the obligations of the altar, so that there will no longer be wrath on the sons of Israel." 

God gave the Israelites many laws concerning gifts, sacrifices, and behavior. These priests, acting as mediators, brought offerings to God on behalf of the Israelites. This was a picture of the greater high priest to come.

King David wrote in the Old Testament that a greater priest would come (Psalm 110). The Psalm makes it clear that the Levitical priesthood, based on the order of Aaron (Moses's brother), was a temporary arrangement, and one day a greater priest would be appointed after the order of Melchizedek (instead of the lineage of the Levites). Since the law was given on the basis of the Levite priests, when the priesthood is changed, of necessity there takes place a change of law also (the Old Covenant) (v 12). So, if the Levite priests are no longer needed, then a new covenant must be established.

For it is evident that Jesus our Lord was descended from the tribe of Judah, not the tribe of Levi. This was a tribe with reference to which Moses spoke nothing concerning priests (v 14). In Exodus 28, God told Aaron and his descendants (the tribe of Levi) that they would serve as priests (Numbers 18). 

Unlike the Levites, and like Melchizedek, Christ's priesthood was not dependent on His lineage: For the one concerning whom these things are spoken belongs to another tribe, from which no one has officiated at the altar (v 13). He was made a priest forever from the promise of God (Psalm 110:4). And this is clearer still, if another priest arises according to the likeness of Melchizedek, who has become such not on the basis of a law of physical requirement, but according to the power of God—an indestructible life (vv 15-16).

Both Jesus and Melchizedek were priests according to the power of God. This new priest (Jesus) from a lineage apart from the Levites created the need for a new covenant.

On their own, the Levitical priests and the Law made nothing perfect. There is a setting aside of a former commandment because of its weakness and uselessness (vv 18-19). Therefore, a better priest and a better covenant were needed. 

The Old Testament Law did, however, serve a purpose: it made the Israelites aware of their sin and pointed towards the work of Christ (through animal sacrifices). But it had no inherent power to forgive sins, make us right before God, or clear our consciences. Therefore, the Pauline Author says the old Law must be set aside because of its weakness and uselessness. 

The author again emphasizes Christ as the new high priest: For it is attested of Him, "You are a priest forever according to the order of Melchizedek" (v 17). The work of Christ and His power as our high priest gives us a much better hope because it offers eternal salvation.

The Levitical priests and the old law have been nullified and we now have a better promise. There is a bringing in of a better hope, through which we draw near to God (v 18). This is the better way to be closer to our Creator through Christ.

The work of Jesus Christ was to save us from our sin and separation from God and brings us to a better hope and a renewed nearness to God. Believing in Jesus is the starting point to this journey. Jesus blazed the trail for us, that we would live like Him and follow in His footsteps, and share in the reward He received (Philippians 2:5-10, Romans 8:17).

We have been delivered from the punishment of our sins, but we are in the process of being totally delivered from the Fall of Man (Genesis 3:23-24), and restored to our original appointment to steward the earth (Hebrews 2:5-8). This is the salvation we do not want to "neglect"(Hebrews 2:3). 

Jesus's goal in saving us is to bring us to glory, to raise us to the position of "Sons" (Hebrews 2:10). We will be restored to the "glory and honor" of reigning with Jesus in His future kingdom if we also live a life of sacrifice (Romans 12:1), in the "suffering of death" with Him, by obeying the Holy Spirit (Hebrews 2:9). This is the better hope our greater, indestructible, forever and eternal priest (Jesus) is leading us to.