So if perfection was through the Levitical priesthood (for on the basis of it the people received the Law), 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)

All covenants exist for the new covenant. The old (conditional) covenant existed for us to seek Christ. The writer of the Book of Hebrews tells us that the new covenant has always been the only eternal covenant because God required faith from the Israelite from the start (Hebrews 3:19). Apostle Paul connects faith with Abraham in Galatians 3, who existed before the Mosaic law. Similarly, the writer connects Christ’s priesthood with Melchizedek, not the Levitical priesthood.

Previously, I mentioned that the writer is building up the argument towards chapter 11. What God has always wanted from His people is faith. However, faith is not a condition which people can meet from their own initiatives. It is the gift from God. Therefore, we can only conclude that God has decided who to save or not before creation. Faith requires the knowledge of God and love for Him. Christ has always been the head of the new creation. Adam had no chance of becoming our head. Adam could not achieve anything by keeping God’s command. As a slave, he was required to obey God but he rebelled because he wanted to become like God. Christ, on the other hand, has never been a slave. He has always been faithful and true.

And I saw heaven opened, and behold, a white horse, and He who sat on it is called Faithful and True, and in righteousness He judges and wages war. (Revelation 19;11)

The orthodox understanding of the covenants is written in Galatians 4. The saints are not under the conditional covenant but the new and eternal covenant. The law (or God’s command in Adam’s case) was never given for us to gain the eternal life.

For, on the one hand, there is the nullification of a former commandment because of its weakness and uselessness (for the Law made nothing perfect); on the other hand, there is the introduction of a better hope, through which we come near to God. (vv. 18-19)

As the eternal High Priest, Christ makes sure we follow His footsteps and helps us to overcome temptations. It is not by keeping the law the saints maintain life in the coming kingdom. We are the children of God because we are united with Christ. Christ’s death is connected to our union with Christ.

Jesus, on the other hand, because He continues forever, holds His priesthood permanently. Therefore, He is also able to save forever those who come to God through Him, since He always lives to make intercession for them. (vv. 24-25)

God gave us the Holy Spirit as the seal of the sonship because He saved us through Christ.

Now He who establishes us with you in Christ and anointed us is God, who also sealed us and gave us the Spirit in our hearts as a pledge. (2 Corinthians 1:21-22)