Objection 1. It would seem that the New Law does not justify. For no man is justified unless he obeys God's law, according to Hebrews 5:9: "He," i.e. Christ, "became to all that obey Him the cause of eternal salvation." But the Gospel does not always cause men to believe in it: for it is written (Romans 10:16): "All do not obey the Gospel." Therefore the New Law does not justify.
Objection 2. Further, the Apostle proves in his epistle to the Romans that the Old Law did not justify, because transgression increased at its advent: for it is stated (Romans 4:15): "The Law worketh wrath: for where there is no law, neither is there transgression." But much more did the New Law increase transgression: since he who sins after the giving of the New Law deserves greater punishment, according to Hebrews 10:28-29: "A man making void the Law of Moses dieth without any mercy under two or three witnesses. How much more, do you think, he deserveth worse punishments, who hath trodden underfoot the Son of God," etc.? Therefore the New Law, like the Old Law, does not justify.
Objection 3. Further, justification is an effect proper to God, according to Romans 8:33: "God that justifieth." But the Old Law was from God just as the New Law. Therefore the New Law does not justify any more than the Old Law.
On the contrary, The Apostle says (Romans 1:16): "I am not ashamed of the Gospel: for it is in the power of God unto salvation to everyone that believeth." But there is no salvation but to those who are justified. Therefore the Law of the Gospel justifies.
I answer that, As stated above (Article 1), there is a twofold element in the Law of the Gospel. There is the chief element, viz. the grace of the Holy Ghost bestowed inwardly. And as to this, the New Law justifies. Hence Augustine says (De Spir. et Lit. xvii): "There," i.e. in the Old Testament, "the Law was set forth in an outward fashion, that the ungodly might be afraid"; "here," i.e. in the New Testament, "it is given in an inward manner, that they may be justified." The other element of the Evangelical Law is secondary: namely, the teachings of faith, and those commandments which direct human affections and human actions. And as to this, the New Law does not justify. Hence the Apostle says (2 Corinthians 3:6) "The letter killeth, but the spirit quickeneth": and Augustine explains this (De Spir. et Lit. xiv, xvii) by saying that the letter denotes any writing external to man, even that of the moral precepts such as are contained in the Gospel. Wherefore the letter, even of the Gospel would kill, unless there were the inward presence of the healing grace of faith.
Reply to Objection 1. This argument holds true of the New Law, not as to its principal, but as to its secondary element: i.e. as to the dogmas and precepts outwardly put before man either in words or in writing.
Reply to Objection 2. Although the grace of the New Testament helps man to avoid sin, yet it does not so confirm man in good that he cannot sin: for this belongs to the state of glory. Hence if a man sin after receiving the grace of the New Testament, he deserves greater punishment, as being ungrateful for greater benefits, and as not using the help given to him. And this is why the New Law is not said to "work wrath": because as far as it is concerned it gives man sufficient help to avoid sin.
Reply to Objection 3. The same God gave both the New and the Old Law, but in different ways. For He gave the Old Law written on tables of stone: whereas He gave the New Law written "in the fleshly tables of the heart," as the Apostle expresses it (2 Corinthians 3:3). Wherefore, as Augustine says (De Spir. et Lit. xviii), "the Apostle calls this letter which is written outside man, a ministration of death and a ministration of condemnation: whereas he calls the other letter, i.e. the Law of the New Testament, the ministration of the spirit and the ministration of justice: because through the gift of the Spirit we work justice, and are delivered from the condemnation due to transgression."
Source: Summa Theologica (New Advent)