One of the important questions in interpreting Paul's understanding of the gospel concerns the manner in which the Law relates to Gentile believers. A lot of it has to do with the interpretation of the statement at Rom 10.4: For Christ is the end of the law so that there may be righteousness for everyone who believes. Is Christ the goal of the law, the fulfillment of the law, the termination of the law?
It seems to me that Paul's picture of salvation contains a continued place for the Law in the life of Christian believers, though this has to be understood in a specific way. Paul says that What was impossible for the law insofar as it was weakened by the flesh, God accomplished sending his Son in the likeness of sinful flesh, and with regard to sin, he condemned sin in his flesh, so that the requirement of the law might be fulfilled in us who do not walk after the flesh but after the Spirit (Rom 8.3). It seems to me that the Law has not been terminated, it has not been entirely eliminated, but that in some great measure it continues to exist and to perform a role in the life of Christians. Christ is the one who accomplishes what the Law was previously unable to do on its own, yet he has an effect on us. In a word, Christ obeys and fulfills the Law for us; we participate in that obedience and fulfillment through our union with Christ, realized and accomplished through the Holy Spirit. Paul also says later that love is the fulfilling of the law (13.10), and he clearly expects Christians to do this (v. 8).
The role of the Law in the life of Christians, then, is an important but mediated one. We participate in Christ's fulfillment of the Law through our participation in his life, death, and resurrection through our union with him. The Law is not terminated or undone or set aside in its entirety; rather, its fulfillment is made possible through Christ and his redemptive work of sanctifying human nature.
What, then, might Paul possibly mean when he says at 6.14 that sin will have no dominion over you, since you are not under law but under grace? He doesn't mean that the Law in its entirety has no presence or role in a Christian's life, and that a Christian is not expected in some significant way to obey the Law. Pay close attention to the preposition he uses: we are not under the Law. The Law is not an oppressive force, it is not a burden, it is not a finger pointing at us. For Christians, liberated by Christ through the Holy Spirit, the Law can be a joy to us. Indeed, insofar as the fruit of the Spirit are love, joy, faithfulness, etc. (Gal 5.22-3), we can say that the Law in its essence becomes a part of our very character. We embody it and obey it.
Of course it is important to realize that our obedience to the Law comes about only through our union with Christ, through the work of the Holy Spirit, and that it is not a condition of the forgiveness of our sins or our right standing before God. When we are baptized, we are baptized into Christ (Gal 3.27) and have assumed a new identity through our union with him. Growing into this new identity of accepted child of God, as led by God, is where the Law comes in, and not in its entirety. (Food laws, circumcision, etc., are not necessary.)