What is the New Covenant?
The primary Old Testament passage pertaining to the New Covenant is Jeremiah 31:31-34. In this wonderful passage God promises to make a New Covenant with His people (v. 31), a covenant unlike the Mosaic covenant (v. 32). Under this New Covenant, God promises to write His laws on the hearts of His people (v. 33), to have intimate communion with them (vv. 33-34), and to forgive their sins (v. 34).
This New Covenant was inaugurated in the sacrificial death of Jesus on the cross. On the night of His betrayal and arrest, Jesus celebrated the Passover with His disciples. During the course of this meal He told them, "This cup which is poured out for you is the new covenant in My blood" (Luke 22:20).
In the New Testament, the book of Hebrews has a great deal to say about this New Covenant. In an article on "Covenant," Trent Butler describes some of the special features of the New Covenant as related in the book of Hebrews :
"The emphasis is on Jesus, the perfect High Priest, providing a new, better, superior covenant (Heb. 7:22; 8:6). Jesus represented the fulfillment of Jeremiah's new covenant promise (Heb. 8:8, 10; 10:16). Jesus was the perfect covenant Mediator (Heb. 9:15), providing an eternal inheritance in a way the old covenant could not (compare 12:24). Jesus' death on the cross satisfied the requirement that all covenants be established by blood (Heb. 9:18, 20) just as was the first covenant (Ex. 24:8). Christ's blood established an everlasting covenant (Heb. 13:20)" (Holman Bible Dictionary, gen. ed. Trent C. Butler (Tennessee: Holman Bible Publishers, 1991), 312).