Do we then overthrow the law by this faith? By no means! On the contrary, we uphold the law. (ESV)
There are people in every generation who love the idea of keeping the law. The attraction is that "If I keep the law, I am able to take credit for being righteous." Those who love this idea of keeping the law we will call legalists. In the time that Paul was writing this verse the legalists were the Pharisees. Jesus called them hypocrites. In our day, legalists are still hypocrites.
Paul knew that this knew revelation of salvation by grace through faith in Jesus Christ was going to get a reaction from the legalists of his day. The argument was that if we are justified (made right with God) apart from keeping the Old Testament law we are overthrowing the Law. It is a fair question: Are Christians law breakers by not insisting on keeping the Law?
The answer is No. Paul says, "On the contrary, we uphold the law." The Law required death as a penalty for law breakers. Jesus, in his death, provides the payment for death that the Law required. Additionally, the original purpose of the Law was to show mankind the need for a Savior. It certainly did that. Finally, through faith in Christ's fulfillment of the Law we have a new ability to keep it.
There will always be legalists. Be wary of them. They will be known for their fingers pointing, while they themselves hold on to secret sins. Their pursuit of being made right by keeping the law will naturally lead to their pride in their own efforts. The saddest thing of all is that they will miss out on true salvation which can only come by faith in the work that Christ has already done.
Are you trying to be made right with God by keeping the Law? How's that working out for you? I encourage you to give up, and accept the work of Christ on your behalf.