The link between the Old Testament and New is problematic for many Christians, and has been since the first century. A typical evangelical view might be summarized as the moral law remains but the ceremonial law has passed away. To which I say, "rubbish!"
The law as a means or a measure of relationship with God, moral, ceremonial or otherwise, is caput, beyond doubt. It never did work as means of achieving rightness with God, and it never could have-- it wasn't meant to. It was no more than a means of restraining the Jews until Christ came, and uncovering for any exposed to it the fundamental sinful nature of mankind. It actually fertilizes our inate sinfulness, and offers no remedy nor instruction as how to overcome it. Those who choose to live by a legal principle, inspired though it may be in the Old Testament, are fallen from grace and apart from the benefits of Christ, even if they call themselves Christian.
Is there some benefit to the Old that is still viable in the realm of the New? Yes, for there is a revelation of God there and the intimation of Christ. People have claimed that the Old Testament God is different than the New, but that is an utter impossibility. There is but one God and he is immutable. What God revealed himself to be in the Old Testament, he still is today and always will be. Any conception from the New Testament cannot be taken to adapt, assuage, adjust, or evolve what God was in the Old.
For some this may present a difficulty. Aligning Old Testament martial characteristics with what appear to be touchy-feely New Testament graces can prove to be a climb up Everest. God, however, does not change and we need to let his self-disclosure speak for itself. With a cat in one arm and a dog in the other, we must wrap our arms around the totality of all he reveals himself to be and embrace God for who he is, majestic and enigmatic. God, as we're introduced to him through our friends Moses and the Prophets, may be a bit scary, but in order to truly know the inviting God of our friends the Apostles, it is incumbent upon us to make new friends but keep the old.