In 2 Timothy 3:16 we read that all Scripture is useful for training in righteousness. That being the case, how are the OT Scriptures "useful" to the Christian living in the age of the New Covenant? Let me suggest three ways [borrowed largely from Douglas Moo]:
First, individual laws from the Mosaic covenant are taken up into the law of Christ. In fact, nine of the Ten Commandments are taken up (albeit in new covenant form) as moral precepts in the law of Christ. It is much like similar individual laws of different countries. For example, both the United States and Canada have laws against murder. However, we would hardly be justified in insisting while under Canadian jurisdiction that its law against murder was really an American law.
Second, Mosaic laws help to fill out the law of Christ where the application of a precept may extend further than what is explicitly set forth in the New Testament. Fred Zaspel gives the example of the NT prohibition against porneia (“sexual immorality”). He indicates that while the range of meaning is not spelled out explicitly in the NT, the OT helps us define the term to include bestiality, incest and other sexually deviant behaviors.
Third, the Mosaic law is an earlier witness in redemptive history to the person and work of Jesus Christ. All of “the Law, the Prophets and the Psalms”(Luke 24:44) should expand our understanding and deepen our delight in and gratitude towards our Savior, who is the figure to which everything in the Scriptures ultimately points. Nothing in the Mosaic law is wasted. Every law serves its purpose honorably in directing us to the One who fulfills it.