“There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit. For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death. For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh: That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.” (Romans 8:1-4 KJV)

There are three laws mentioned in this text:
1. “The law of the Spirit of life in Christ Jesus.”
2. “The law of sin and death.”
3. “The law.”

The first law is the same as “The law of liberty” (Jas. 1:25; 2:12); “The law of Christ” (Gal. 6:2; 1 Cor. 9:21). We are indeed under law to Christ in this age. It is the law that we are expected do and by which we will be judged.

The second law is the law that Paul had to struggle with while is under “the law” and without Christ (Rom. 7:22-24) from which the third law (the law) could not give him relief.

The third law (“the law”) is the law of Moses, which Paul simply called “the law” most of the time.

So, what “the law” (of Moses) could not do, the law of the Spirit life/Liberty/Christ did. That is it freed him from “law of sin” in his members that produced spiritual death in him. “The law” could not take away that sin and its dominion over him. That was done when he submitted himself to the law of Christ.