CCC 1965 The New Law or the Law of the Gospel is the perfection here on earth of the divine law, natural and revealed. It is the work of Christ and is expressed particularly in the Sermon on the Mount. It is also the work of the Holy Spirit and through him it becomes the interior law of charity: “I will establish a New Covenant with the house of Israel. .. I will put my laws into their hands, and write them on their hearts, and I will be their God, and they shall be my people.”1

CCC 1966 The New Law is the grace of the Holy Spirit given to the faithful through faith in Christ. It works through charity; it uses the Sermon on the Mount to teach us what must be done and makes use of the sacraments to give us the grace to do it:
If anyone should meditate with devotion and perspicacity on the sermon our Lord gave on the mount, as we read in the Gospel of Saint Matthew, he will doubtless find there. .. the perfect way of the Christian life. .. This sermon contains. .. all the precepts needed to shape one’s life.2

CCC 1967 The Law of the Gospel “fulfills,” refines, surpasses, and leads the Old Law to its perfection.3 In the Beatitudes, the New Law fulfills the divine promises by elevating and orienting them toward the “kingdom of heaven.” It is addressed to those open to accepting this new hope with faith – the poor, the humble, the afflicted, the pure of heart, those persecuted on account of Christ and so marks out the surprising ways of the Kingdom.

CCC 1968 The Law of the Gospel fulfills the commandments of the Law. The Lord’s Sermon on the Mount, far from abolishing or devaluing the moral prescriptions of the Old Law, releases their hidden potential and has new demands arise from them: it reveals their entire divine and human truth. It does not add new external precepts, but proceeds to reform the heart, the root of human acts, where man chooses between the pure and the impure,4 where faith, hope, and charity are formed and with them the other virtues. The Gospel thus brings the Law to its fullness through imitation of the perfection of the heavenly Father, through forgiveness of enemies and prayer for persecutors, in emulation of the divine generosity.5

1 Heb 8:8, 10; cf. Jer 31:31-34.
2 St. Augustine, De serm. Dom. 1, 1: PL 34,1229-1230.
3 Cf. Mt 5:17-19.
4 Cf. Mt 15:18-19.
5 Cf. Mt 5:44,48.