Just finished reading an article on the Law in Dictionary of Jesus and the Gospels by Doug Moo. Although a vast subject, I thought his conclusion was helpful in understanding the Law as it relates to the Old and New Covenants.
“In different ways and with different emphases, all four Gospels reflect a dominant theme in the teaching of Jesus: his divine authority with reference to the Law. Jesus was quick to clarify that his authority did not negate the role of the Law in salvation history. But he also made it clear that this authority involved the right not only to exposit, add to or deepen the Law, but to make demands of his people independent of that Law. This being the case, it is quite inadequate, and potentially misleading, to think of Jesus as “the last great expositor of the Law.” The Law, God’s great gift to Israel, anticipated and looked forward to the eschatological teaching of God’s will that Jesus brought. This teaching, not the Law, is the focus of the Gospels, and the Law remains authoritative for the disciple of Jesus only insofar as it is taken up into his own teaching.” (Dictionary of Jesus and the Gospels, 461)