Christians are "new covenant" believers. Christ gave us new laws as part of the new covenant. We don't have to obey the Law of Moses.
There is only a single place where Messiah says He gives a new commandment:
"A new commandment I give to you, that you love one another, even as I have loved you, that you also love one another. By this all men will know that you are My disciples, if you have love for one another." (John 13:34)
While love among believers is to be a sign of discipleship, it is not a new commandment. We are told, "love your neighbor as yourself" in Leviticus 19:18.
As far as the new covenant itself, God says that He will write His Law upon the hearts of those in that covenant (Jeremiah 31:31-33).
As far as the Law of Christ versus the Law of Moses, we address that claim in another article.
If you still have questions, check out our definitions and assumptions page. If you still have questions or concerns after reading that, please contact us. We would love the opportunity to understand and respond to those concerns!