The old covenant comprises testimonies and prophecies regarding the second and the last covenants of God. That's why Jesus declared that we should keep up with the scriptures which include the books of Moses, the prophets, and the psalms (meaning apocryphas and deoterocanonicals are not included). However, regarding the new despensation in Christian era, the birth of Jesus is the birth of new priesthood. And there was change in the law. This law was imposed to the second covenant of God - the Christians. Because Israel apostatized. And a new law supersedes the law of Moses in the old covenant. But this doesn't necessarily mean to throw away the old covenant.