Does the New Testament override the Old Testament?

Prior to this "setting aside" of the law, Jesus says that "whoever relaxes one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever does them and teaches them will be called great in the kingdom of heaven. For I tell you, unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven" (Matt 5:19, 20). If He did in fact dismiss the Law, it seems He would have been condemning Himself. He then says that you have to be more righteous than the Pharisees, who spent their lives following the law, to ever enter Heaven.

In Mark 7:8-13 we see Jesus accusing the Pharisees of dismissing the law:

"You leave the commandment of God and hold to the tradition of men." And he said to them, "You have a fine way of rejecting the commandment of God in order to establish your tradition! For Moses said, 'Honor your father and your mother'; and, 'Whoever reviles father or mother must surely die.' But you say, 'If a man tells his father or his mother, "Whatever you would have gained from me is Corban"' (that is, given to God)-- then you no longer permit him to do anything for his father or mother, thus making void the word of God by your tradition that you have handed down. And many such things you do."

The rabbis would always build their teachings upon the teachings of those who came before them; theoretically at least, all their teachings came ultimately from Moses. Jesus did things differently: "You have heard... but I say to you..." (note that in doing so He claims to be God, as only God could correct the law)

Jesus did not abolish the Law of Moses (He even commanded obedience to the Pharisees): He claimed that it did not fully represent the righteous requirements of God, but sets a minimum standard; even a person who kept every single command is not necessarily in right standing with God. For example, in Mark 10 we find:

And Pharisees came up and in order to test him asked, "Is it lawful for a man to divorce his wife?" He answered them, "What did Moses command you?" They said, "Moses allowed a man to write a certificate of divorce and to send her away." And Jesus said to them, "Because of your hardness of heart he wrote you this commandment. But from the beginning of creation, 'God made them male and female.' 'Therefore a man shall leave his father and mother and hold fast to his wife, and the two shall become one flesh.' So they are no longer two but one flesh. What therefore God has joined together, let not man separate." And in the house the disciples asked him again about this matter. And he said to them, "Whoever divorces his wife and marries another commits adultery against her, and if she divorces her husband and marries another, she commits adultery."

Moses allowed for divorce "if she finds no favor in his eyes because he has found some indecency in her..." but that doesn't mean God is OK with divorce: He hates it. In Matthew 5:32 and 19:9 we see that divorce is allowed for sexual immorality, and in Ezra 10 He commanded it as part of a cleansing of Israel, but Jesus says here that God intends marriage, but divorce is a result of our sin. Even though God allows it doesn't mean He likes it.

Jesus is not saying that we no longer need the law; He says that we need something more than the law, concluding this sermon with "you must be perfect, as your heavenly Father is perfect" (Matt 5:48). According to Christianity, Jesus is that something more.

I think it pertinent to quote more from Matthew 5 because it in essence answer the question. I have added emphasis where it comes applicable to the answer.

The Fulfillment of the Law

17“Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19*Anyone who breaks one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven.* 20For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven.

Murder

21“You have heard that it was said to the people long ago, ‘Do not murder,a and anyone who murders will be subject to judgment.’ 22But I tell you that anyone who is angry with his brotherb will be subject to judgment. Again, anyone who says to his brother, ‘Raca,c’ is answerable to the Sanhedrin. But anyone who says, ‘You fool!’ will be in danger of the fire of hell.

23“Therefore, if you are offering your gift at the altar and there remember that your brother has something against you, 24leave your gift there in front of the altar. First go and be reconciled to your brother; then come and offer your gift.

25“Settle matters quickly with your adversary who is taking you to court. Do it while you are still with him on the way, or he may hand you over to the judge, and the judge may hand you over to the officer, and you may be thrown into prison. 26I tell you the truth, you will not get out until you have paid the last penny.d

Adultery

27“You have heard that it was said, ‘Do not commit adultery.’e 28But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart. 29If your right eye causes you to sin, gouge it out and throw it away. It is better for you to lose one part of your body than for your whole body to be thrown into hell. 30And if your right hand causes you to sin, cut it off and throw it away. It is better for you to lose one part of your body than for your whole body to go into hell.

Divorce

31“It has been said, ‘Anyone who divorces his wife must give her a certificate of divorce.’f 32But I tell you that anyone who divorces his wife, except for marital unfaithfulness, causes her to become an adulteress, and anyone who marries the divorced woman commits adultery.

Oaths

33“Again, you have heard that it was said to the people long ago, ‘Do not break your oath, but keep the oaths you have made to the Lord.’ 34But I tell you, Do not swear at all: either by heaven, for it is God’s throne; 35or by the earth, for it is his footstool; or by Jerusalem, for it is the city of the Great King. 36And do not swear by your head, for you cannot make even one hair white or black. 37Simply let your ‘Yes’ be ‘Yes,’ and your ‘No,’ ‘No’; anything beyond this comes from the evil one.

An Eye for an Eye

38“You have heard that it was said, ‘Eye for eye, and tooth for tooth.’g 39But I tell you, Do not resist an evil person. If someone strikes you on the right cheek, turn to him the other also. 40And if someone wants to sue you and take your tunic, let him have your cloak as well. 41If someone forces you to go one mile, go with him two miles. 42Give to the one who asks you, and do not turn away from the one who wants to borrow from you.

Love for Enemies

43“You have heard that it was said, ‘Love your neighborh and hate your enemy.’ 44*But I tell you: Love your enemies and pray for those who persecute you*, 45that you may be sons of your Father in heaven. He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous. 46If you love those who love you, what reward will you get? Are not even the tax collectors doing that? 47And if you greet only your brothers, what are you doing more than others? Do not even pagans do that? 48Be perfect, therefore, as your heavenly Father is perfect.

It becomes clear in these passages that Jesus Law did not override the Old Testament, but in fact where just like clarifications or additions. Amendments if you will

Christ did not simply do away with the law, he ended or fulfilled it. Jesus is the substance of the shadows, the anti type of the types, and the very epitome of all the moral enunciation of the law. Jesus said, "Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfill" (Matt. 5: 17). Notice the next verse, "For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled" (vs. 18). Jesus fulfilled the law and inaugurated his system or testament (Lk. 24: 44, 47). Christ's system is not without law, but the onerous system of Moses was nailed to Jesus' cross (Gal. 6: 2, Col. 2: 14, see addendum). Jesus' apostles are "able ministers of the new testament" (2 Cor. 3: 6). The Law of Moses could not impart life (2 Cor. 3: 7-18). The law was only a "schoolmaster to bring us (Jew, dm) unto Christ, that we might be justified by faith" (Gal. 3: 24). "But after that faith is come," Paul continued, "we are no longer under a schoolmaster" (vs. 25). Paul warned regarding any who would attempt justification by the Law of Moses. Hear him: "Christ is become of no effect unto you, whosoever of you are justified by the law; ye are fallen from grace" (Gal. 5: 4). One cannot be saved by a system of meritorious works that seek to earn salvation and by grace at the same time (Rom. 11: 6). John said, "For the law was given by Moses, but grace and truth came by Jesus Christ" (Jn. 1: 17)

Peace to all; Just to point out 3 problems in the conclusion that the Law is done away with. First only 1 part of the OT (The decalog) = 10 commandments constitute the LAW. 2nd The word Law was mistranslated from the word TORAH which means Teachings, or Instructions. 3rd If you believe any of G-d's WORD is done away with then the one we believe is the WORD made flesh divided His Kingdom. If HE was the WORD before He came down then He had to be that same WORD when He arrived, which He refers to when He said "Untill Heaven and earth disappear Not a jot or line will disappear from the Torah" Which at the time was the only written word of God which would naturally have JOTs and LINEs in it. Keep in mind whenever the Christian Bible mentions LAW it should say Torah unless it is speaking about a certian commandment. Also something that may help your perspective is as followes when He said "In the last days men will be (Lawless") substitute the word (TORAHLESS) which is the actual word used by Messiah Yeshua! You would have to know the original Aramaic/Hebrew to have known that. Hope I blessed you!

LOVE PAUL

The new covenant throws out the baby with the bathwater. That's why it's new. It throws out the ten commandments and it throws out the rest of the law also. There is no OT law that NT Christians are bound to obey. The new covenant completely overrides and does away with the old.

The OT law was given to the Hebrews only, and was fulfilled by the Jewish Messiah. It was never given to the Gentiles. There is no passage in the OT or NT that ever says Gentile Christians need to follow the law.

You have all read your bibles. You know that not only is salvation by grace, but we live the Christian life by grace. We do not live it by works, or by any law. We are free from the law.

There are differing views on this, including

• all laws of the Old Testament are still binding
• some OT laws remain, some don't (this is the most common view)
• OT laws aren't meant for Christians at all

For a more thorough explanation of these views, who supports them and on what basis, see my answer on:
Do we have to obey the laws of the bible? If so, what laws?

This should be considered additive to what @Mason Wheeler said. He beat me to that part of it, and his answer was good, but I think it can be expanded on just a little bit more to bring it into focus and clear up all doubt.

The Law of Love (Matthew 22:34-40) in the New Testament actually fulfills all of the points of the Old testament law, it does not do away with them.

If you love God, you will not have any other gods before Him, you won't take his name in vain, you will keep his Sabbath, etc. If you love your neighbor, you won't lie, cheat, steal, covet, etc.