Jesus said that the Old Testament law was in force until the time of John the Baptist but since then the Kingdom of God is being proclaimed (Luke 16:16; see also Matthew 11:12-13).
Jesus said that he was the fulfilment of the Old Testament law. "Do not think that I have come to abolish the law or the prophets; I have come not to abolish but to fulfil." (Matthew 5:17). He then goes on to say “For truly I tell you, until heaven and earth pass away, not one letter, not one stroke of a letter, will pass from the law until all is accomplished.” (Matthew 5:17-18) Was he saying that the Old Testament law remains in force and that every command should be obeyed by Christians today? Well, the good news is that no Christians today think that we should follow every rule contained in the Old Testament law.
Jesus said that the Old Testament law could be summed up in the two great commandments "Love God with all your heart, all your soul, all your mind and all your strength." and "Love your neighbour the same way that you love yourself" (Matthew 22:37-40; Luke 10:27). He also introduced what we now call “The Golden Rule” and indicated that it, too, summed up the law. "In everything, do to others as you would have them do to you; for this is the law and the prophets." (Matthew 7:12)
Jesus has authority over everything and his commands must be obeyed. At the end of Matthew’s gospel Jesus is recorded as saying that all authority in heaven and earth have been given to him. He then instructed the apostles to teach new disciples “to obey everything that I have commanded you”.(Matthew 28:18-20). So there is no question: obedience to Jesus’ teaching is more important for Christians today than attempting to keep the Old Testament law. Does God speak to us, today, through the Old Testament? Yes, of course he does. But that doesn’t mean that we have to carefully examine every word of the Old Testament and try to apply it to our lives.
Jesus didn’t say anything about the New Testament. He did say that the Holy Spirit would continue to teach his followers after he had left. However there is no suggestion that this indicated that particular books would be written.