New covenant theology is a hermeneutic, a lens as it were by which the scriptures and the gospel is viewed and understood. The essence of the this paradigm is that Jesus is the new lawgiver. The 10 commandments were surely a law, but that law was nothing more than a document of the covenant that God made with man. That document established an objective righteousness providing then a means for Jesus to visibly satisfy all righteousness. When Jesus accomplished the work of the law vicariously for His people, He then vicariously died to atone for their sins and thus established a New and Better covenant–a covenant of faith and not of works. The ramifications on the believer's life are huge and alter many known doctrines. Because Christ has established a New Covenant and if then the old has passed away, then the rule of law falls not to Moses, but to Christ, which is exactly what we find in the Sermon on the Mount in Matthew 5-7.
"In speaking of a new covenant, he makes the first one obsolete. And what is becoming obsolete and growing old is ready to vanish away."
Listen to Josh Preach on this very subject of New Covenant Theology.
Watch below a sermon defining New Covenant Theology from Douglas Goodin