“For sin will have no dominion over you, since you are not under law but under grace.”
Please don’t misread this verse and think that you have a promised, sinless perfection in this life. It’s simply a promise that sin will not eventually triumph over the lives of those who follow Jesus. Followers of Jesus are no longer under the Mosaic law where sin regularly triumphed over good. To the contrary, Christians live under a much more powerful motivator to conquer sin than law. That power is called “grace."
Under law, a person feels he must try to conquer sin by mere human effort. You try harder and harder, only to fail continually. It creates a cycle of despair, for no one can eventually keep the entire law.
But grace is different. Christians now try to obey the law, not because we have to, but because we want to. The motivator is grace. The stimulus is love in response to the one who loved us deeply.
Grace always trumps sin. That’s Paul’s message to us all in this verse.