Because we have left our old life behind, we should not “let sin reign” or have control over our mortal bodies. The word for mortal is θνητός meaning liable to death. Our bodies therefore are still subject to death even though death does not rule and have power over the whole of our lives (v12). We are not to allow any part of our life to be used for wicked purposes but should serve the cause of righteousness with all that we are. This introduces a theme of offering ourselves picked up later in chapter 12. We offer ourselves to God, not to evil (v13).
We are no longer under the rule and influence of sin, it is not our lord. Paul links this with no longer being under the Law but under grace. The idea is that we have been transformed to one kingdom, that of sin and death which uses the Law as its constitution and the kingdom of God where Grace provides the constitution.
Faithroots 