Only the priesthood is applied in that change.
"For when there is a change of the priesthood,
there must also be a change of the law." (Hebrews 7:12 NIV )
There is a great deal more that is changed than the tribe of the priests. Are Christians commanded to sacrifice animals as offerings to God for peace, atonement, sins, and so forth? No. Those laws are changed. They are abrogated in fact.
Are we beginning to commend ourselves again? Or do we need, like some people, letters of recommendation to you or from you? You yourselves are our letter, written on our hearts, known and read by everybody. You show that you are a letter from Christ, the result of our ministry, written not with ink but with the Spirit of the living God, not on tablets of stone but on tablets of human hearts. (2 Corinthians 3:1-3 NIV )
Now if the ministry that brought death, which was engraved in letters on stone, came with glory, so that the Israelites could not look steadily at the face of Moses because of its glory, fading though it was, will not the ministry of the Spirit be even more glorious? If the ministry that condemns men is glorious, how much more glorious is the ministry that brings righteousness! For what was glorious has no glory now in comparison with the surpassing glory. And if what was fading away came with glory, how much greater is the glory of that which lasts! Therefore, since we have such a hope, we are very bold. We are not like Moses, who would put a veil over his face to keep the Israelites from gazing at it while the radiance was fading away. But their minds were made dull, for to this day the same veil remains when the old covenant is read. It has not been removed, because only in Christ is it taken away. Even to this day when Moses is read, a veil covers their hearts. But whenever anyone turns to the Lord, the veil is taken away. Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom. And we, who with unveiled faces all reflect the Lord's glory, are being transformed into his likeness with ever-increasing glory, which comes from the Lord, who is the Spirit. (2 Corinthians 3:7-18 NIV )
We ought return to the thread's topic, which is not the abrogation of some of the laws of Moses but the real presence of the Lord Jesus Christ in the holy eucharist.