In order to know our part in the New Covenant, we need to have in mind the big contrast of the law and grace. This is the difference of the two main covenants in the Bible, the Old Covenant of the law and the New Covenant of grace. We are not under the Old Covenant but under the New one. We cannot fulfill our part of the New covenant by keeping the terms of the Old. If we think, that unless we don’t keep the commandments we are breaking our covenant with God, or if we obey the law then we keep our part of the covenant, then we are trying to fulfill the New Covenant with the terms of the Old. Not knowing in clarity the contrast of law and grace we are trying to obey God in the terms of the Old Covenant though we are under the New one.
The Old Covenant is the Covenant of the law. A Covenant that was made between God and the people of Israel. Under the Old unless they didn’t obey all the commandments they were breaking it. One single commandment they disobeyed was enough to break it with the result to be cursed. Paul in his letter to the Galatians says that anyone under the law was cursed simply because no one can be justified by the obedience of the law. Doing your part under the law/Old Covenant was a mission impossible.
The New Covenant is the gospel of grace. A Covenant made between God the Father and His Son Jesus Christ. It’s an eternal Covenant that cannot be ever been broken. Whosoever believes in Jesus comes under the blessings of the New Covenant. Your part in the Covenant is Jesus. Grace means God does something on your behalf. Grace is not a doctrine or another teaching but it’s Jesus Himself. He is , He did and does all on your behalf in the New Covenant. That’s why is called gospel(good news).
The big contrast of the Old from the New is this: Under the Old it was all up to you to obey the law but in the New is everything up to Jesus. Jesus fulfills always perfectly your part. There is nothing for you to do but to rest. No work from you is accepted in the New Covenant. There is nothing for you to achieve in the New but to receive all that Jesus achieved for you. Rest in the fact that Jesus is your part in the New Covenant. Rest in the fact that Jesus is for you all you need to be. Rest in the fact that Jesus did all that was needed to be done for you. When you rest He works for you and through you. This is the obedience of the New Covenant. It’s called obedience of the gospel or obedience of faith.