The law given to Moses at Sinai was abrogated with the advent of the new covenant. To put it a better way: The entirety of the Mosaic Covenant was fulfilled in Christ. The law of Moses no longer serves as direct and immediate judge over the lives and conduct of God's people. God's children today obey the Law of Christ [Gal 6.2, 1 Cor 9:21].
Jesus, who is better than Moses, in his sermon on the mount served as the new law giver establishing his new commandments [Matt 5:19]. In that sermon he expounded on the law that Jer 31 said would be written in the believer's inward parts. The law written on man's heart is vastly different than the ministration of death written on tablets of stone [2 Cor 4:7]. The former comes as a result of God's gracious gift of faith which results in the new birth. The latter was a non-gracious covenant with terms that were "obey or perish" [Gal 3:12].
Significant passages related to distinction and supremacy of new covenant over old.
For the priesthood being changed, there is made of necessity a change also of the law. Hebrews 7:12
The writer of Hebrews had the word "better" in mind when he wrote his epistle. Christ is better than angels, Joshua, Moses, and Aaron. The change in the law came as a result of a better law giver. One whose laws would be obeyed because of a changed heart. The old covenant had absolutely no power over the flesh.
Rom 8:3 For what the law couldn’t do, in that it was weak through the flesh, God did, sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh;
For if that first covenant had been faultless, then should no place have been sought for the second. Hebrews 8:7
Again, the supremacy of the second, or new covenant. The fault laid in man's inability to obey God, not in God's law which was a reflection of His character.
In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away. Hebrews 8:13 (KJV)
The writer of Hebrews warns those who considered abandoning Christ and going back to following the law by pointing out that it was about to disappear.
Lastly, I need to be clear on the entirety of the law's fulfillment in Christ. I mention that because some traditions divide the Mosaic law into three general categories: civil, moral, and ceremonial laws, as if some laws may still apply while others were abrogated. In God's word you'll find no such divisions.
Hos 6:6 For it is love that I seek, and not sacrifice; knowledge of God more than burnt offerings.