For the law was given by Moses, but grace and truth came by Jesus Christ. ~ John 1:17
The law of Moses was national Israel’s covenant until Christ, through whom the new covenant has been established. The law of God (God’s ways – righteousness, truth, mercy, judgements, etc.,) is eternal.
The law of Moses was given to Israel as a tutor to teach them God’s law (God’s ways as mentioned above) and was the conduit of God’s law until Christ. Consequently Israel was under carnal ordinances (Hebrews 9:10) which were given to teach them the ways of God. These carnal ordinances were such things as the sacrificial system, the priesthood, the feast days, etc. These were all types and shadows pointing to Christ, and continued until the time of reformation when Christ fulfilled God’s law by giving himself as the offering for our sins and becoming our great high priest.
Because of Jesus we do not keep the ordinances instructed the law of Moses for the children of Israel in the Old Testament. We are not required to bring an unblemished goat to a temple in Jerusalem where an appointed priest offers it as a sin offering on our behalf. We simply look to Jesus in repentance when we sin, and his precious blood cleanses us from all sin because Jesus gave himself as the offering for our sins when he died on the cross.
The law of God requires atonement for sin. The law of Moses taught this lesson through the sacrifices and the priesthood, but Jesus fulfilled God’s law regarding atonement by giving his innocent life for our sins. Now there is no longer any need for the tutor (the law of Moses) to instruct us how to have our sins atoned for. Jesus has fulfilled God’s law and we come to Jesus for forgiveness and are reconciled to God through him.
The law of God is eternal and is now administered through the grace of Christ and not through the law of Moses (by the newness of the Spirit and not the oldness of the letter). The law of God administrated through the law of Moses was written on tables of stone. The law of God through Christ is now written in our hearts.