Now if perfection had been attainable through the Levitical priesthood (for under it the people received the law), what further need would there have been for another priest to arise after the order of Melchizedek, rather than one named after the order of Aaron? For when there is a change in the priesthood, there is necessarily a change in the law as well.
Hebrews 7:11-12 (ESV)
The Law of Christ is not the same as the Law of Moses.
According to Hebrews, the Law is a foreshadowing of good things to come, namely a New Covenant from God that removed the deadly consequences of sin once and for all by Jesus’ perfect sacrifice (Hebrews 10:1-4).
The New Covenant is not an extension of the Old Covenant, but an entirely new and better covenant. As believers, we do not follow the Old Covenant, with its Aaronic priesthood and sacrificial system. Rather, we follow Jesus who is our Great and Eternal High Priest of the New Covenant in the order of Melchizedek, not Aaron.
Since there is a change of priesthood, there is a change of the law as well.
While the Law of Moses was for a particular group of God’s people, the Law of Christ is for all of God’s people. The Law of Christ is more than just a new standard of righteousness. It is a much higher and perfect standard than the Law of Moses because it is Christ who works His supernatural love into and through us. Having said that, we fulfil the Law of Christ (Galatians 6:2) through loving one another just as Christ loves us (John 13:34-35).
Christ gives us the grace and power we need to accomplish His will.
We have a divine advantage because His Spirit is actively and intimately shaping our hearts and minds with the living Law of Christ. Thus, obedience is the fruit of God’s life and love abiding in us. This is something that the Law of Moses could not do for us.