Paul’s central theme in the books of Galatians and Romans is justification by faith. When Paul wrote these books, many early believers were emerging from a religious practice where righteousness was earned strictly through adherence to the law. It must have been powerful to hear Paul announce that justification by faith and justification by keeping the law are mutually exclusive. Christ’s crucifixion and resurrection covered the law so that only the believer’s faith is required.

Christ has redeemed us from the curse of the law, having become a curse for us (for it is written, “Cursed is everyone who hangs on a tree”), that the blessing of Abraham might come upon the Gentiles in Christ Jesus, that we might receive the promise of the Spirit through faith. – Gal. 3:13-14

Believers are free from the law as a means of salvation, from its external ceremonial regulations as a way of living, and from its curse for disobedience to the law—a curse that Christ bore for all believers. This freedom is not, however, a license to sin. 

For you, brethren, have been called to liberty; only do not use liberty as an opportunity for the flesh, but through love serve one another. – Gal. 5:13

When a person is convicted of a capital crime and executed, the law has no further claim on that person. It is the same with the believer who has died in Christ (who paid the penalty for the believer’s sins in full) and rises to new life in Him—justice has been satisfied and the believer is forever free from any further penalty. 

We were therefore buried with Him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life. – Rom. 6:4

When a person trusts in Christ for salvation, that person spiritually participates with the Lord in His crucifixion and His victory over sin and death. The believer’s old self is dead, having been crucified with Christ. The believer’s new self has the privilege of the indwelling Christ empowering and living through them.

But you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. Now if anyone does not have the Spirit of Christ, he is not His. – Rom. 8:9

The crucifixion of Christ was a one-time historical fact with continuing results into eternity. Christ’s sacrificial death provides eternal payment for all believers’ sins, and does not need to be supplemented by any human works.

Also there were many priests, because they were prevented by death from continuing. But He, because He continues forever, has an unchangeable priesthood. Therefore He is also able to save to the uttermost those who come to God through Him, since He always lives to make intercession for them. – Heb. 7:23-25