The only of the 10 commandments that was not carried forward to the new testament defining what sin was was specifically the admonition to keep the Sabbath. That was because of what the religious order of Jesus day had done to the tradition of Sabbath keeping. In fact, God, through Christ, went out of His way on occasion to specifically annoy the religious order in their Sabbath traditions by healing on the Sabbath and then commanding the man who was healed to take up his bed and carry it home.
The rest is still there in the new testament. The old testament commandments relating to food are gone because the Jewish people were not wandering about as nomads any longer. The old testament rules for sacrifice that were implemented to specifically cover the people's sin and acknowledge God are gone since Christ paid the price on the cross to do this. Everything else is still there. In fact, over and over again in the sermon on the mount Christ used a phrase similar to - you have heard it said ----, but I say unto you ---- where His standards and thus the standards of the new testament were higher and tougher than what was imposed in the old testament for how people should treat each other, specifically because He had come and was in the process of showing them how it was possible to live righteously and because He would send the Holy Spirit to in-dwell believers and, if they obeyed His promptings, lead them on the right path. Clearly, most don't and they will answer for that before God one day. The higher the position of authority, the more they will have to answer for.
But the law still remains as it is what will be used on the day of the great white throne judgment at the end of the recorded history in the Bible when God judges those who did not accept His plan of salvation before sending them to hell for eternity.
The new covenant is simply the final means of salvation which was alluded to from the time of man's downfall in the garden of Eden. It doesn't eliminate the definitions of sin that cause people to need salvation in the first place, and it certainly gives no indication that God treats it any more lightly on an eternal basis.