In what sense can believers claim to be "dead to the law"?
We know God's law is just and holy and good. It shows us our responsibility to love God perfectly and to love our neighbor as ourselves. It sets this standard as the guide and the goal of our conduct. We see this standard displayed perfectly in Christ, our Lord and Savior, therefore, our goal is to be conformed to Him. By this standard, the law exposes our sinfulness and shows us our need of Christ and His blood and righteousness as the only ground of salvation.
Believer's are justified by God based on the righteousness of Christ. The law, therefore, is not our enemy. God's law is our enemy only when we seek to attain justification and life by our deeds of the law (Romans 3:19-20; Galatians 3:10). The law curses every sinner who seeks salvation or any part of it based on anything other than the merits of Christ. The same law pronounces all who come to God, "the Judge of all" (Hebrews 12:23), pleading the righteousness of Christ alone, righteous and holy. Believers are "dead to the law" in that the law no longer curses them nor pronounces them legally defiled because their debt has been paid by Christ.
Does the law require anything from a believer?
It requires every justified sinner to love God perfectly and to love our neighbors as ourselves. It requires obedience and godliness. But it requires none of these things for the purposes of saving ourselves, keeping ourselves saved, sanctifying ourselves or making ourselves holier or more qualified for Heaven, nor does it require obedience aimed at making our salvation sure, nor for earning any rewards from God. All of these things are already accomplished by the grace of God based on the righteousness of Christ. Our works and efforts to obey the law are not good enough to accomplish any of these things. They are to be attributed to God's grace as the fruit and effect of Christ's righteousness alone (Ephesians 1:3; Colossians 2:9-10). As believers, we are to seek to obey the law out of gratitude and love for God who has freely given us all these great blessings based upon what Christ did for us. In this way God is glorified, Christ is exalted, and we are encouraged in obedience and godliness with no room for boasting (Philippians 3:3).