Objection 1. It would seem that the New Law does not fulfil the Old. Because to fulfil and to void are contrary. But the New Law voids or excludes the observances of the Old Law: for the Apostle says (Galatians 5:2): "If you be circumcised, Christ shall profit you nothing." Therefore the New Law is not a fulfilment of the Old.
Objection 2. Further, one contrary is not the fulfilment of another. But Our Lord propounded in the New Law precepts that were contrary to precepts of the Old Law. For we read (Matthew 5:27-32): You have heard that it was said to them of old:... "Whosoever shall put away his wife, let him give her a bill of divorce. But I say to you that whosoever shall put away his wife... maketh her to commit adultery." Furthermore, the same evidently applies to the prohibition against swearing, against retaliation, and against hating one's enemies. In like manner Our Lord seems to have done away with the precepts of the Old Law relating to the different kinds of foods (Matthew 15:11): "Not that which goeth into the mouth defileth the man: but what cometh out of the mouth, this defileth a man." Therefore the New Law is not a fulfilment of the Old.
Objection 3. Further, whoever acts against a law does not fulfil the law. But Christ in certain cases acted against the Law. For He touched the leper (Matthew 8:3), which was contrary to the Law. Likewise He seems to have frequently broken the sabbath; since the Jews used to say of Him (John 9:16): "This man is not of God, who keepeth not the sabbath." Therefore Christ did not fulfil the Law: and so the New Law given by Christ is not a fulfilment of the Old.
Objection 4. Further, the Old Law contained precepts, moral, ceremonial, and judicial, as stated above (Question 99, Article 4). But Our Lord (Matthew 5) fulfilled the Law in some respects, but without mentioning the judicial and ceremonial precepts. Therefore it seems that the New Law is not a complete fulfilment of the Old.
On the contrary, Our Lord said (Matthew 5:17): "I am not come to destroy, but to fulfil": and went on to say (Matthew 5:18): "One jot or one tittle shall not pass of the Law till all be fulfilled."
I answer that, As stated above (Article 1), the New Law is compared to the Old as the perfect to the imperfect. Now everything perfect fulfils that which is lacking in the imperfect. And accordingly the New Law fulfils the Old by supplying that which was lacking in the Old Law.
Now two things of every law is to make men righteous and virtuous, as was stated above (Question 92, Article 1): and consequently the end of the Old Law was the justification of men. The Law, however, could not accomplish this: but foreshadowed it by certain ceremonial actions, and promised it in words. And in this respect, the New Law fulfils the Old by justifying men through the power of Christ's Passion. This is what the Apostle says (Romans 8:3-4): "What the Law could not do... God sending His own Son in the likeness of sinful flesh... hath condemned sin in the flesh, that the justification of the Law might be fulfilled in us." And in this respect, the New Law gives what the Old Law promised, according to 2 Corinthians 1:20: "Whatever are the promises of God, in Him," i.e. in Christ, "they are 'Yea'." [The Douay version reads thus: "All the promises of God are in Him, 'It is'."] Again, in this respect, it also fulfils what the Old Law foreshadowed. Hence it is written (Colossians 2:17) concerning the ceremonial precepts that they were "a shadow of things to come, but the body is of Christ"; in other words, the reality is found in Christ. Wherefore the New Law is called the law of reality; whereas the Old Law is called the law of shadow or of figure.
Now Christ fulfilled the precepts of the Old Law both in His works and in His doctrine. In His works, because He was willing to be circumcised and to fulfil the other legal observances, which were binding for the time being; according to Galatians 4:4: "Made under the Law." In His doctrine He fulfilled the precepts of the Law in three ways. First, by explaining the true sense of the Law. This is clear in the case of murder and adultery, the prohibition of which the Scribes and Pharisees thought to refer only to the exterior act: wherefore Our Lord fulfilled the Law by showing that the prohibition extended also to the interior acts of sins. Secondly, Our Lord fulfilled the precepts of the Law by prescribing the safest way of complying with the statutes of the Old Law. Thus the Old Law forbade perjury: and this is more safely avoided, by abstaining altogether from swearing, save in cases of urgency. Thirdly, Our Lord fulfilled the precepts of the Law, by adding some counsels of perfection: this is clearly seen in Matthew 19:21, where Our Lord said to the man who affirmed that he had kept all the precepts of the Old Law: "One thing is wanting to thee: If thou wilt be perfect, go, sell whatsoever thou hast," etc. [St. Thomas combines Matthew 19:21 with Mark 10:21.
Reply to Objection 1. The New Law does not void observance of the Old Law except in the point of ceremonial precepts, as stated above (13, 3,4). Now the latter were figurative of something to come. Wherefore from the very fact that the ceremonial precepts were fulfilled when those things were accomplished which they foreshadowed, it follows that they are no longer to be observed: for it they were to be observed, this would mean that something is still to be accomplished and is not yet fulfilled. Thus the promise of a future gift holds no longer when it has been fulfilled by the presentation of the gift. In this way the legal ceremonies are abolished by being fulfilled.
Reply to Objection 2. As Augustine says (Contra Faust. xix, 26), those precepts of Our Lord are not contrary to the precepts of the Old Law. For what Our Lord commanded about a man not putting away his wife, is not contrary to what the Law prescribed. "For the Law did not say: 'Let him that wills, put his wife away': the contrary of which would be not to put her away. On the contrary, the Law was unwilling that a man should put away his wife, since it prescribed a delay, so that excessive eagerness for divorce might cease through being weakened during the writing of the bill. Hence Our Lord, in order to impress the fact that a wife ought not easily to be put away, allowed no exception save in the case of fornication." The same applies to the prohibition about swearing, as stated above. The same is also clear with respect to the prohibition of retaliation. For the Law fixed a limit to revenge, by forbidding men to seek vengeance unreasonably: whereas Our Lord deprived them of vengeance more completely by commanding them to abstain from it altogether. With regard to the hatred of one's enemies, He dispelled the false interpretation of the Pharisees, by admonishing us to hate, not the person, but his sin. As to discriminating between various foods, which was a ceremonial matter, Our Lord did not forbid this to be observed: but He showed that no foods are naturally unclean, but only in token of something else, as stated above (102, 6, ad 1).
Reply to Objection 3. It was forbidden by the Law to touch a leper; because by doing so, man incurred a certain uncleanness of irregularity, as also by touching the dead, as stated above (102, 5, ad 4). But Our Lord, Who healed the leper, could not contract an uncleanness. By those things which He did on the sabbath, He did not break the sabbath in reality, as the Master Himself shows in the Gospel: both because He worked miracles by His Divine power, which is ever active among things; and because He worked miracles by His Divine power, which is ever active among things; and because His works were concerned with the salvation of man, while the Pharisees were concerned for the well-being of animals even on the sabbath; and again because on account of urgency He excused His disciples for gathering the ears of corn on the sabbath. But He did seem to break the sabbath according to the superstitious interpretation of the Pharisees, who thought that man ought to abstain from doing even works of kindness on the sabbath; which was contrary to the intention of the Law.
Reply to Objection 4. The reason why the ceremonial precepts of the Law are not mentioned in Matthew 5 is because, as stated above (ad 1), their observance was abolished by their fulfilment. But of the judicial precepts He mentioned that of retaliation: so that what He said about it should refer to all the others. With regard to this precept, He taught that the intention of the Law was that retaliation should be sought out of love of justice, and not as a punishment out of revengeful spite, which He forbade, admonishing man to be ready to suffer yet greater insults; and this remains still in the New Law.
Source: Summa Theologica (New Advent)