New Covenant Theology–Must We Obey a New Law?

[This article was revised in January 2019: Further information.]

New Covenant Theology teaches that Jesus Christ fulfilled the law, and that by fulfilling it, He ended it. But some within New Covenant Theology have also taught that Jesus instituted a new law that we must obey. Is there a new law with new commands that Jesus has given us under the New Covenant? If so, must we obey these commands?