The old covenant that Israel was under was built around the Mosaic Law that God gave to the Israelites in the wilderness after their Exodus from Egypt. This law was binding until Christ came and ushered in the new covenant, which we are under today. The Jews were devoted to the law and cherished it (cf. Ps. 119:43-48). Under the new covenant, the law is still important in that it expounds on holiness, but we are not bound by it.
There was a stark problem with the law. It demanded absolute adherence and obedience to its provisions. The law thus showed the people their sin, but it provided for atonement and forgiveness in only a limited way. It pointed ahead to God’s ultimate solution for sin but did not provide that solution itself.
The new covenant, however, set aside the old and revealed the fullness of God’s grace and mercy. Since we could not satisfy the demands of the old covenant, Jesus fulfilled it for us and gave us a new covenant that reconciles us with God by grace through faith. The new covenant is not about keeping a set of rules, but about trusting and loving the Lord Jesus Christ (Bible Expositor and Illuminator Union Gospel Press, Spring Quarter 2022).