Justin Taylor does gives a good summary how the New Covenant is actually a different covenant (and a better covenant - (Heb. 7:22) and a superior covenat (Heb. 8:) than the Old Covenant while maintaining God's unity of purpose across the covenants. Since the New Covenant is made with a reconstituted covenant people (Matthew 21:33-43, Romans 9-11) that involves a new order(Hebrews 9:10), and a new set of governing laws and principles. The establishment of the New Covenant has made the Old Covenant with its stipulations obsolete (2 Corinthians 3:14, Hebrews 8:13, 9:1, etc.).
It a middle ground approach (neither Covenantal or Dispensational) that I believe is very profitable. it will relieve you from the logical fallacies of Classical Covenant Theology or Classical Dispensational Theology.