The key to Christian life and living, and therefore to all moral theology, is put so well by Aquinas: the New Law is the grace of the Holy Ghost, written on our hearts. By His power we are enabled to live as we should, thus fulfilling all that Christ taught us. To quote from the Common Doctor's Summa Theologiæ (I-II, 106, 1, sed contra & resp.):
The New Law is the law of the New Testament. But the law of the New Testament is instilled in our hearts. For the Apostle, quoting the authority of Jeremiah 31:31-33: "Behold the days shall come, saith the Lord; and I will perfect unto the house of Israel, and unto the house of Judah, a new testament," says, explaining what this statement is (Hebrews 8:8-10): "For this is the testament which I will make to the house of Israel... by giving My laws into their mind, and in their heart will I write them." Therefore the New Law is instilled in our hearts.
I answer that, "Each thing appears to be that which preponderates in it," as the Philosopher states (Ethic. ix, 8). Now that which is preponderant in the law of the New Testament, and whereon all its efficacy is based, is the grace of the Holy Ghost, which is given through faith in Christ. Consequently the New Law is chiefly the grace itself of the Holy Ghost, which is given to those who believe in Christ. This is manifestly stated by the Apostle who says (Romans 3:27): "Where is... thy boasting? It is excluded. By what law? Of works? No, but by the law of faith": for he calls the grace itself of faith "a law." And still more clearly it is written (Romans 8:2): "The law of the spirit of life, in Christ Jesus, hath delivered me from the law of sin and of death." Hence Augustine says (De Spir. et Lit. xxiv) that "as the law of deeds was written on tables of stone, so is the law of faith inscribed on the hearts of the faithful": and elsewhere, in the same book (xxi): "What else are the Divine laws written by God Himself on our hearts, but the very presence of His Holy Spirit?"
Nevertheless the New Law contains certain things that dispose us to receive the grace of the Holy Ghost, and pertaining to the use of that grace: such things are of secondary importance, so to speak, in the New Law; and the faithful need to be instructed concerning them, both by word and writing, both as to what they should believe and as to what they should do. Consequently we must say that the New Law is in the first place a law that is inscribed on our hearts, but that secondarily it is a written law.