The New Covenant must be included in our descriptions of Biblical covenantal theory, as it is the completion and fulfillment of all the preceding covenants. Likewise, it is also the only covenant since the Adamic which has universal influence, impacting all of humanity.
However, also keep in mind that we do not have the New Covenant as neatly written in the Bible as the previous covenants. This is due to a number of causes: the suzerain system had evolved into a Roman contractual system; we have no actual written documents from Jesus Himself; and most of the preaching of Jesus was done to those still under the Mosaic Covenant, and are more directly applicable to them than to the New Covenant which He would usher in later in His ministry.
That said, the New Testament still very clearly defines the covenant terms, and often refers back to the old methodologies of covenant theology to draw a link between Moses and the Christ.
The New Covenant (various scriptures)
Suzerain Party - God the Father
Vassal Party - All men who choose to accept it (bilateral)
Broker/Mediator for Vassals - Jesus
Right to Serve as Broker - Only individual in history to be both fully-human and fully-God
Preamble (John 1:1-5; Heb 8:15)
In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things came into being through Him, and apart from Him nothing came into being that has come into being. In Him was life, and the life was the Light of men. The Light shines in the darkness, and the darkness did not comprehend it. (John 1:1-5)
For this reason He is the mediator of a new covenant, so that, since a death has taken place for the redemption of the transgressions that were committed under the first covenant, those who have been called may receive the promise of the eternal inheritance. (Heb 8:15)
The preamble identifies the parties and their relationship to one another. As always with Biblical covenants, God is the suzerain party, and mankind is the vassal. Jesus Christ is the mediator between man and God, and His identity as both fully human and fully God makes Him perfectly fit to act as the mediator between the two parties.
Historical Prologue (entire Old Testament; John 3:16-17)
For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life. For God did not send the Son into the world to judge the world, but that the world might be saved through Him. (John 3:16-17)
The historical prologue recalls the history of how the suzerain has shown benevolence to the vassal in the past. Actually, the entire Old Testament and all four Gospels—Matthew, Mark, Luke and John—record for us the numerous ways in which God has demonstrated His benevolence toward mankind, and demonstrates His right to enact this covenant. However, the most common, briefest, and perhaps most beautiful statement of God’s benevolence toward mankind is demonstrated in the passage of John recorded in chapter 3.
Conditions and Terms
But what does it say? "THE WORD IS NEAR YOU, IN YOUR MOUTH AND IN YOUR HEART"--that is, the word of faith which we are preaching, that if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved; for with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation. …For there is no distinction between Jew and Greek; for the same Lord is Lord of all, abounding in riches for all who call on Him; for "WHOEVER WILL CALL ON THE NAME OF THE LORD WILL BE SAVED." (Romans 10:8-10, 12-13)
And [the jailor] called for lights and rushed in, and trembling with fear he fell down before Paul and Silas, and after he brought them out, he said, "Sirs, what must I do to be saved?" They said, "Believe in the Lord Jesus, and you will be saved, you and your household." (Acts 16:29-31)
The terms of the New Covenant are straightforward, and are written in numerous ways throughout the New Testament. The four passages above clearly outline the process tell how one accepts the New Covenant. Accepting the New Covenant is what Jesus calls being “born of the Spirit” John 3:5-6; the two passages above lay out the required steps one must take in order to be born of the Spirit and accept the New Covenant:
1. Call upon God for the forgiveness of sin;
2. Submit to the Lordship of Jesus;
3. Confess your submission publicly; and
4. Believe in the Resurrection.
Numbers 1, 3, and 4 are self-explanatory, though some wonder what number 2 might entail. Jesus says that submission to Him and love of Him implies that you will keep His commandments (John 14:15). Note that this (following the commandments of Jesus) is not a requirement to be joined to the covenant, but it is something which we are pledged to do; failure to do so will result in potential punishment by our suzerain.
Witness of the Covenant
The Bible records two witnesses to the New Covenant: baptism and the Eucharist. These are the expected witnesses and signs by which the Covenant shall be remembered and announced to the world. Each of these signs alludes to Old Testament signs: baptism is a parallel of circumcision (a sign of the Abramic Covenant), and the Eucharist is a parallel of Passover (a sign of the Mosaic Covenant).
And Jesus came up and spoke to them, saying, "All authority has been given to Me in heaven and on earth. Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit, teaching them to observe all that I commanded you; and lo, I am with you always, even to the end of the age." (Matthew 28:18-20)
The first sign is Baptism, whereby we first publicly accept the New Covenant. The Didache tells us that the first century Christians practiced baptism by immersion in running water if possible, in standing water as a backup, and by pouring water over the head if no other method existed.
And when He had taken some bread and given thanks, He broke it and gave it to them, saying, "This is My body which is given for you; do this in remembrance of Me.” And in the same way He took the cup after they had eaten, saying, "This cup which is poured out for you is the new covenant in My blood.” (Luke 22:19-20)
The second sign is the Lord’s Supper (aka, the Eucharist, or Communion). It is implied strongly in Acts 2:42, Acts 20:7, and 1Cor 11:20 that this should be celebrated every week. Communion is also frequently "closed" by various denominations to only those within their denomination; I can find absolutely no evidence for that in Scripture or ancient Christianity. If you read the Dictionary of Early Christian Beliefs, I find over 50 early church references to communion within the first 150 years of Christianity, not a single one of which references closing communion to those of different church bodies or with differing ideas. The only thing I can find is speaking out against unbelievers partaking of the bread and cup, for these are signs of our covenant with Christ, and not to be profaned by the unsaved.
Curses and Blessings
“For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life. For God did not send the Son into the world to judge the world, but that the world might be saved through Him. He who believes in Him is not judged; he who does not believe has been judged already, because he has not believed in the name of the only begotten Son of God.” (John 3:16-18)
The blessing associated with the acceptance of the New Covenant is eternal life; the curse for not accepting is that the person will be judged for their sins and, if found lacking, be separated from God (i.e., reside in Hell) for eternity. Since Romans 3:23 predicts that all men will be found lacking if judged, then the New Covenant must be accepted in order to receive eternal life—there is no other pathway to reach eternal life (cf. John 14:6).