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Could you kindly direct me to where the W.C.F. speaks specifically of the Covenant of Redemption. I have had a quick browse through and I can't seem to find it.
Lets see if it is in Scripture? Though the "phrase is not in Scripture (as is neither, total depravity, unconditional election, limited atonement, irresistible grace, perseverance of the saints, Calvinism, etc) the theological truth is. The whole counsel of God concerning all things necessary for his own glory, man's salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture (WCF 1.6).

The phrase, Covenant of Redemption (CR) historically in the Reformed tradition refers to the intertrinitarian covenant—particularly the covenant between the Father and the Son before the foundation of the world. CR took place in eternity and is the plan by which election would be elective. Berkhof defines CR as, “the agreement between the Father giving the Son as head and redeemer of all the elect and the Son voluntarily taking the place of those whom the Father has given Him.” Thus, God, foreseeing the fall, in His loving grace effects a covenant with the Son in which He gave all the elect to the Son and the Son willingly says I will take their place. Is this seen in Scripture? Yes, Eph 1:4-7, 11; 1 Pet 1:19-20; Rev 13:8? These are self-explanatory IMO, but what about the OT?

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Psalm 2:7-9 I will tell of the decree: Jehovah said unto me, Thou art my son; This day have I begotten thee. Ask of me, and I will give thee the nations for thine inheritance, And the uttermost parts of the earth for thy possession. Thou shalt break them with a rod of iron; Thou shalt dash them in pieces like a potter's vessel.
In this royal messianic Psalm God the Father is giving to the Son the nations as His inheritance and is appointing the Son. This is special language of royal enthronement. This is one reason why Christ can give us the command in Matt 28:18-20 (… make disciples of all the nations …). God is saying I have appointed you now as the sovereign over all your inheritance—all the chosen people. And so the Son takes the role of Mediator and of head (compare; Psa 40:7-9; Psa 89:3; Heb 10:5-7). See the NC is a fulfillment of the OCs. It is the fulfillment of God’s ONE plan! However, God’s plan has a history (redemptive history—covenant history) which is critical to our maturity in Christ!

Additionally, look at the Gospels. Christ emphasizes that the Father had given Him work to do.

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John 5:36 But the witness which I have is greater than that of John; for the works which the Father hath given me to accomplish, the very works that I do, bear witness of me, that the Father hath sent me.
The Father gave Jesus a work to do. Throughout the Gospels we see Christ saying things like, “My meat is to do the will of him that sent me, and to accomplish his work” (John 4:34). Jesus the Son continuously is subordinating His will to the Father’s will. Remember the Garden of Gethsemane, “nevertheless not my will, but thine, be done, (Luke 22:42)? But, do we not ask ourselves is not the Jesus the very God of very God? Is He is not equal in power and glory with God the Father? Of course, so what is Jesus saying? He is simply referring to the obligations of the covenant which He voluntarily took on Himself in order to save His people. Thus, simply The Covenant of Redemption is an eternal covenant—that covenant which is prior to time, in which the Son undertakes to be our surety and our mediator and the Father undertakes to give to the Son all the elect because of the Son’s perfect obedience.

Reformed and Always Reforming,