Sin will have no dominion over you, since you are not under law but under grace. — Romans 6:14 (ESV)
For some reason, most Christians believe that we have to obey the Law. But here Paul writes plainly that we “are not under the law”. That means we are free from living our lives trying to follow it. This verse says if you live your life trying to follow the Law, sin wins. That is, you will remain a captive of sin. But as a follower of Jesus, you are called to live under grace. This is the only way to appropriate a new King in your life.
It is impossible to emphasize this point too much. Not only are the righteous requirements of the Law fulfilled in you by faith in Jesus (who established this as the new covenant); not only are you made new by getting a new heart, dying and rising again to be a new creation; but also, the strategy for living righteously changed. Before, you tried your hardest to obey the Law. Now you live a life of love, walking in intimacy with your Lover, being led by the Head!
This is a different way of living. Instead of growing in legalism or perfectionism, which is a life of living in a straight-jacket, we are to grow in love for our Lord, which frees us to follow our heart, which seeks to show our love to the object of our affection by living our lives to give Him joy. The way of the heart is the way of abundant life, as long as our heart seeks to honor the only one worthy of such a great affection. To give your heart to a lesser love may lead to greater misery than living under the Law. Jesus came that we might have life, and have it abundantly (John 10:10), but there is only one way to have it, and that is to give our heart fully to Him, and walk under grace, and not under the law.