But at the very start, by saying a slave of Jesus Christ, Paul wants to make it very clear that even though we're free of the bondage of the Mosaic Law, we aren't free from obedience to Jesus Christ. We are owned by Him. He told the Corinthians, I'm going to read to you 2 Corinthians 5:15, he says, "He died for all, that those who live should live no longer for themselves, but for Him who died for them and rose again." So we aren't our own.
The fact that we have been saved by grace doesn't mean it's now a free picnic. We get to do whatever we want to do. He died for us and redeemed us so that we no longer live for ourselves, but we live for Him.