These are some meditations from Romans 6 answering the question:
If our sins are forgiven, what is then our new relationship with sin?

Salvation has affected our relationship with sin in many ways, the one that Romans 6 mostly focuses on is its lost of power in our lives.

1. Because of this idea of free costly grace talked in Romans 5, Paul clarifies emphatically that this does mean a license to sin. This grace does not mean lawlessness.
2. We have been united with the death and resurrection of Christ; those who have died have been freed as well from sin.
3. Since we have died with Christ, we have the benefits of this new life through Christ.

What a glorious thing, the gospel saves us from the penalty of sin, and helps us come out from being under the power of sin.