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.
Source: Catechism of the Catholic Church (Vatican.va)