For the law of the Spirit of life in Christ Jesus has liberated you from the law of sin and death.
- Romans 8:2
The law of sin and death is the old law mentioned in the verse above. I believe it is the tyrannical rule of sin in the life of all unsaved people. It seems as though this is the same “law of sin” which remains with Paul even after his conversion (Romans 7:21, 23, 25).
For an unbeliever, this old law rules every part of the being: soul, mind, and body. For the saved person, this old law’s remnants can be found in the mind and body. This is because the believer’s soul is presently completely redeemed, his mind is presently in the process of redemption, and his body is not yet experiencing any redemption.
But when the Holy Spirit enters a person at the point of conversion, the Spirit ushers in a new law of freedom from the old law. The law of freedom is written by the justifying work of Jesus Christ. The work of Jesus overrides the tranny of sin and death and begins a rule of freedom to do God’s will. I believe that the Holy Spirit so impresses this new law upon the Christian that he or she cannot help but become more like Christ.
For what the Law could not do, weak as it was through the flesh, God did: sending His own Son in the likeness of sinful flesh and as an offering for sin, He condemned sin in the flesh,
- Romans 8:3
What was the work that Jesus did? The Lord completely fulfilled the Law of God as a man. He did the work required for righteousness. He did so without flaw. Jesus in the flesh was strong to perfectly fulfill God’s requirements for holiness.
In contrast, all other human beings of all time were not strong enough in the flesh to fulfill the Law. Rather when any other person but Jesus encountered the Law of God, sin rose up within that individual and produced sin (Romans 7:7, 8). As a result of produced sin, the individual became condemned to death and slavery to sin. All other flesh but the flesh of Christ was too weak to be righteous through the Law. The Law was “weak” in all other flesh in that it stirred up the sin nature within the individual.
Christians are under the rule of the very Spirit of Jesus Christ. As such, the fulfillment of the Law that Christ accomplishes in the flesh, is applied to all who believe in Him. This is why Jesus fulfilled the Law.
…in order that the requirement of the Law might be fulfilled in us, who do not walk according to the flesh, but according to the Spirit.
Romans 8:4 (NASB)
 The old law is the tyranny of sin. The new law is the freedom from sin found in Christ. Neither refers to the Law of God.