A few more thoughts while I have a little time.
The new covenant is usually regarded as the outworking of the Covenant of Grace (also called the Eternal Covenant, Covenant of Peace or Council of Redemption). It may be helpful to quote from the WCF Larger Catechism:
Q.30. Doth God leave all mankind to perish in the estate of sin and misery?
Ans. God doth not leave all mankind to perish in the estate of sin and misery, into which they fell by the breach of the……. covenant of works; but of His mere love and mercy delivereth His elect out of it, and bringeth them into an estate of salvation by the second covenant, commonly called the covenant of grace.
Q.31. With whom was the Covenant of Grace made?
Ans. The Covenant of Grace was made with Christ as the second Adam, and in Him with all the elect as His seed.
What we find is that God the Father, in eternity, has given to Christ a vast number of sinners to redeem. We see this in John 6:39 and also in John 17:24. "Father, I desire that they also whom you gave Me may be with Me where I am, that they may behold My glory which You have given Me...." Not even one of those given by the Father to the Son will be lost; every last one will be redeemed. This is also spelled out in Eph. 1:3-14, where we see that the Holy Spirit was also involved, sealing Christ's people for salvation at the Last Day.
All this was determined, before ever there was a world, in the Covenant of Grace. That is why Paul can say of the Thessalonians, ‘But we are bound to give thanks to God always for you, brethren beloved by the Lord, because God from the beginning chose you for salvation through sanctification by the Spirit and belief in the truth’ (2Thes 2:13 ). The whole of the Bible may be seen as the outworking of this great covenant and the accomplishment of God’s gracious plan for our salvation.
References to the Covenant of Grace can be found in various parts of the Bible if one is prepared to look for them as the following examples will show:-
Luke 22:22. “And truly the Son of Man goes as it has been determined……” Determined where and by whom if not in the Covenant of Grace?
John 6:38-39. “For I have come down from heaven, not to do My own will, but the will of Him who sent Me. This is the will of the Father who sent Me, that of all He has given Me I should lose nothing, but should raise it up at the last day.” Christ has been given a people and the task by the Father which He is determined to fulfil. What can this refer to if not the Covenant of Grace?
John 10:16. “And other sheep I have which are not of this fold; them also I must bring, and they will hear My voice; and there will be one flock and one shepherd.” Not, “I will bring,” but, “I must bring.” Our Lord had been given a commission to fulfil.
John 10:17-18. “Therefore My Father loves Me, because I lay down My life that I may take it again. No one takes it from Me, but I lay it down of Myself. I have power to lay it down, and I have power to take it again. This command I have received from My Father.” Where did Christ receive this command, the doing of which merited so well the Father’s love? In the Covenant of Grace, of course.
Phil 2:6-8 (my translation). ‘Who, being in the form of God, did not consider equality with God something to be held to His advantage, but made Himself of no reputation, taking the form of a bondservant, and coming in the likeness of men. And being found in appearance as a man, He humbled Himself and became obedient to the point of death, even the death of the cross.’ In the Covenant of Grace, our Lord gave up temporarily that equality with the Father that had existed from all eternity, and became the willing servant of Exodus 21:5-6 and Psalm 40:6-8 in order to rescue those who had been given to Him (John 17:2, 6 ).
Heb 2:13. ‘Here am I and the children whom God has given to Me.’ Given by the Father to the Son in the Covenant of Grace to be redeemed from sin and brought to heaven.
A helpful book on this subject is The Divine Covenants by A.W. PInk. Here is an excerpt:
‘God made covenants with Noah, Abraham, David; but were they, as fallen creatures able to enter into covenant with their august and holy Maker? Were they able to stand for themselves, or to be sureties for others? The very question answers itself. What, for instance, could Noah possibly do which would ensure that the earth should never be destroyed again by a flood? These subordinate covenants were nothing more or less than the Lord’s making manifest, in an especial and public manner, the grand covenant: making known something of its glorious contents, confirming their own personal interest in it, and assuring them that Christ, the great covenant Head, should be of themselves and spring from their seed.
‘This is what accounts for that singular expression which occurs so frequently in Scripture: “Behold, I establish My covenant with you and your seed after you” (Gen 9:9 ). Yet there follows no mention of any conditions, or work to be done by them: only a promise of unconditional blessings. And why? Because the “conditions” were to be fulfilled and the “work” was to be done by Christ, and nothing remained but to bestow the blessings upon His people. So when David says, “He hath made with me an everlasting covenant” (2Sam 23:5 ) he simply means, God had admitted him into an interest in the everlasting covenant and made him partaker of its privileges. Hence it is that when the apostle Paul refers to the various covenants which God had made with men in Old Testament times, he styles them not “covenants of stipulations” but “covenants of promise”‘
Tow other helpful books on Covenant Theology from a credobaptist perspective are:
Covenant Theology from Adam to Christ (RBAP, 2005) which contains two 17th Century works: Nehemiah Coxe's A Discourse of the Covenants and an extract from John Owen's mammoth commentary on Hebrews 8:3-16.
The Distinctiveness of Baptist Covenant Theology by Pascal Denault (SGCB, 2013 in my copy, but I believe there has been a more recent revision).