The New Covenant is a specific Covenant made to Israel for the Millennial reign of Christ.
The New Testament, the shedding of Christ's blood, is the basis for the New Covenant, but the New Testament isn't the New Covenant.
The Bible says that God has made the First Covenant old - it is decayed and vanishing away (Heb 8:13). Jesus is the mediator of the New Covenant "which was established upon better promises" (Heb 8:6).
The First Covenant "had ordinances of divine service, and a worldly sanctuary" (Heb 9:1) "in which were offered both gifts and sacrifices, that could not make him that did service perfect" (v.9). This stuff has all disappeared and has been replaced by the perfect sacrifice of Jesus Christ.
The first covenant is old, decayed, and gone. We are now under the new covenant becasue Jesus "NOW has obtained a more excellent ministry, by how much also he IS the mediator of a better covenant" (Heb 8:6).
Wills contain covenants. A new will revokes an old will. The covenants (promises) in an old will are superseded by the covenants (promises) in the new will. Jesus' will to us is the New Testament containing the new covenant of promise, "that by means of death...that they which are called might receive the promise of eternal inheritance" (Heb 9:15). We are now no longer under the old covenant of earthly high priests and tabernacles, but under the new covenant of Christ, our high priest and heavenly tabernacle.