Jesus was still living, and fulfilling, the mosaic law during the time when he was alive. The Messiah was prophesied to fulfill the law in its entirety therefore he lived by means of the law at that time.
However, after his death, the mosaic law became void for God had dismantled it and made his Son the means for approach to God.
Jesus spoke about this on the night before his death...he said 'he is giving them a new commandment' and he also said he is making a 'new covenant' Luke 22:29 and I make a covenant with YOU, just as my Father has made a covenant with me, for a kingdom, 30 that YOU may eat and drink at my table in my kingdom, and sit on thrones to judge the twelve tribes of Israel.
That was in harmony with the prophecy of Jeremiah that God will give the nation a new covenant unlike the mosaic law covenant. Jeremiah 31:“...and I will conclude with the house of Israel and with the house of Judah a new covenant; 32 not one like the covenant that I concluded with their forefathers in the day of my taking hold of their hand to bring them forth out of the land of Egypt, ‘which covenant of mine they themselves broke..."
this is why the apostle Paul could speak of the Mosaic law as being finished and a new covenant put in place thru Christ as its mediator
Hebrews 8:6 But now [Jesus] has obtained a more excellent public service, so that he is also the mediator of a correspondingly better covenant, which has been legally established upon better promises.
7 For if that first covenant had been faultless, no place would have been sought for a second; 8 for he does find fault with the people when he says: “‘Look! There are days coming,’ says Jehovah, ‘and I will conclude with the house of Israel and with the house of Judah a new covenant; 9 not according to the covenant that I made with their forefathers in [the] day of my taking hold of their hand to bring them forth out of the land of Egypt, because they did not continue in my covenant, so that I stopped caring for them,’ says Jehovah.”
10 “‘For this is the covenant that I shall covenant with the house of Israel after those days,’ says Jehovah. ‘I will put my laws in their mind, and in their hearts I shall write them. And I will become their God, and they themselves will become my people
It was necessary for Christ to live by the mosaic law code when he was alive in order to fulfill it. He fulfilled it by living perfectly by it...no other human could do that which is why a new covenant was needed... the new covenant would be based on faith and not on obedience to a set of prescribed laws. So christians are certainly not required to keep following the mosaic law...they are required to put faith in the new covenant and live the life that Jesus lived... a life of love and devotion to God and to ones fellow man.