New covenant theology is best described as a hermeneutical principle, or an interpretative grid through which one reads and interprets the Scriptures. As a hermeneutical principle, it stands as a bridge between dispensational theology and covenant theology. That is not to say that new covenant theology has intentionally set itself up between dispensational theology and covenant theology, but that new covenant theology shares things in common with both dispensational and covenant theology. As such, we cannot say what new covenant theology is without reference to dispensational theology and covenant theology.
Dispensational theology essentially sees the Scriptures unfolding in a series of, usually, seven “dispensations.” A dispensation can be loosely defined as the means through which God governs His actions with man and creation. Therefore, God’s governance was different with Adam than it was with Abraham, etc. Dispensational theology views the revelation as progressive, i.e., in each dispensation, God reveals more and more of His divine plan of redemption. However, while Scripture is a progressive revelation, each successive dispensation represents a new way of God dealing with His creation. In other words, according to dispensational theology, there is a strong level of discontinuity between the dispensations; once an old dispensation is over and a new one begun, the "old" way of doing things under the old dispensation is superseded by the new dispensation. And each dispensation is typically introduced with some new revelation from God.
The thing to remember with dispensational theology is that there is a sharp distinction between Israel and the Church. They are two different people with two different destinies in God’s economy. The Church is seen as a "parenthesis" between God’s dealings with national Israel. The restored kingdom promised to Israel will be fulfilled in the Millennium. Until then is the Church Age—the time of the Gentiles.
Covenant theology is effectively the polar opposite of dispensational theology. While both agree that Scripture is progressive, the overarching principle of covenant theology is the covenant. Covenant theology sees two theological covenants in Scripture—the covenant of works and the covenant of grace. The covenant of works was introduced in the Garden between God and man in which God promised mankind life for obedience and judgment for disobedience. The covenant of works was re-introduced at Sinai as God promised Israel long life and blessing in the land on the condition of their obedience to the Mosaic covenant, but expulsion and judgment in the event of their disobedience. The covenant of grace was implemented after the fall and represents God’s unconditional covenant with man to redeem and save the elect. All of the various biblical covenants (Noahic, Abrahamic, Mosaic, Davidic, and the New) are outworkings of the covenant of grace as God works His plan of redemption in human history. So, where dispensational theology saw a discontinuity between the various dispensations (and in particular between the Old and the New Testaments), covenant theology sees a great deal of continuity.
This is especially evident in the fact that covenant theology does not see a sharp distinction between Israel and the Church. Both entities are seen as one continuous people of God with one ultimate destiny.
All of that serves as the backdrop to view new covenant theology. As mentioned previously, new covenant theology is a middle point between the two. It shares a lot in common with classic covenant theology, in particular the continuity between the Church and Israel as being one people of God. However, it also differs from covenant theology in that it does not necessarily view the Scriptures as the unfolding of redemption in a covenant of works/covenant of grace framework. Instead, it sees the Scriptures in a more promise/fulfillment paradigm.
By far the biggest difference between new covenant theology and covenant theology is how each views the Mosaic Law. Covenant theology sees the Law in three ways: civil, ceremonial and moral. The civil aspect of the Law was those laws in the covenant of Sinai which governed the theocratic nation of Israel while they live in the Promised Land. The ceremonial aspect of the Law governed the worship of God by Israel while in the land. Finally, the moral aspect of the Law governed the behavior of God’s people. It should be understood that the Law, in and of itself, is one cohesive whole and that the Jews did not delineate between civil, ceremonial and moral; these are just terms used to help identify the three areas of Israelite life that the Mosaic Law governed.
According to classic covenant theology, Jesus came to fulfill the Law (Matthew 5:17). He did so by satisfying all of the ceremonial, civil and moral aspects of the Law. Jesus Christ is the reality behind the shadows of the Old Testament sacrificial system and thereby fulfills the ceremonial aspect of the Law. Jesus Christ also bore the penalty our sins deserved and thereby fulfilled the civil aspect of the Law. Finally, Jesus Christ lived in full accordance with the moral aspect of the Law and fulfilled the righteous requirements of the Law.
Now, the moral aspect of the Law represents the essence of the covenant of works. As such, it transcends the Mosaic economy. In other words, God has always required holiness from humanity. The covenant of works was not negated due to the fall, nor was it negated even though it was fulfilled in Christ. The moral aspect of the Law still stands as the standard of morality for mankind because it is reflective of God’s character, and that does not change. Therefore, covenant theology still sees the Mosaic Law (especially the Ten Commandments) as prescriptive for the Church, even though the ceremonial and civil aspects have been rendered obsolete in Christ.
New covenant theology sees the Mosaic Law as a whole and sees it all fulfilled in Christ (so far in agreement with covenant theology). However, because new covenant theology sees the Mosaic Law as a whole, it also sees the moral aspect of the Mosaic Law as fulfilled in Christ and no longer applying to Christians. Instead of being under the moral aspect of the Mosaic Law as summarized in the Ten Commandments, we are under the law of Christ (1 Corinthians 9:21). The law of Christ would be those prescriptions that Christ specifically stated in the Gospels (e.g., the Sermon on the Mount). In other words, the entire Mosaic economy has been set aside in new covenant theology; it no longer applies in any way to Christians. So, while covenant theology sees a continuity between the Old and New Testaments in regards to God’s people and the way of salvation, new covenant theology draws a rather sharp line of distinction between the Old and New Testaments when it comes to the difference between the old Mosaic covenant and the new covenant mediated by Christ. The old covenant is obsolete (including the moral aspect of the Mosaic Law) and replaced by the new covenant with the law of Christ to govern its morality.