The idea that the Father entered into a 'covenant of redemption' with the Son in eternity is a staple of Reformed covenant theology. As typically expressed, the Father appointed the Son Mediator and Surety of the covenant of grace and promised him a glorious reward on completion of his redemptive work. This construction is found in the work of early covenant theologian, Johannes Cocceius, seventeenth century Orthodox Reformed divines, old Princeton theologians, Charles and A. A. Hodge, and more recently, Louis Berkhof.
However, Robert Letham complains that as traditionally explained the 'covenant of redemption' is open to a number of criticisms. It seems to entail the eternal subordination of the Son to the Father, and as the pactum salutis (pact of salvation) is taken only to concern the Father and the Son, with little or no mention of the Holy Spirit, it is sub-trinitarian. Indeed, in his The Work of Christ, (endnote 34, p. 254), Letham points out that in his Outlines of Theology, (p. 371-372), A. A. Hodge makes no reference at all to the Holy Spirit in his discussion of the covenant of redemption. Charles Hodge defends the notion of the Father entering into a pre-temporal pact with the Son by invoking the doctrine of the Trinity (Systematic Theology Volume 2, p. 359). But, once more, when it comes to the substance of the 'covenant of redemption', the doctrine is unfolded in terms of an arrangement between the Father and the Son. The Father is said to give the Holy Spirit to the Son to facilitate the work of redemption, but that is about as far as it goes. Louis Berkhof's treatment of the 'covenant of redemption' likewise pays scant attention to the role of the Holy Spirit, (Systematic Theology, p. 265-271). He defines the compact thus, the agreement between the Father, giving the Son as Head of the elect, and the Son, voluntarily taking the place of those whom the Father had given Him. (Italics original, p. 271). As Berkhof's definition makes no mention of the Holy Spirit, it clearly falls foul of the principle that both the internal and external acts of the Trinity are undivided. On this basis the 'covenant of redemption' in its traditionally stated form is highly problematic.
Now we come to Herman Bavinck. The Dutch dogmatician is critical of some aspects of the construction of the pactum salutis found in Orthodox Reformed divines such as Cocceious. But he nevertheless sees a clear biblical basis for the idea that in eternity the Father appointed the Son as Mediator (amongst other texts, he cites: Isaiah 42:1, John 6:38-40, 10:18, 1 Peter 1:20, Revelation 13:8). As he develops his teaching on the 'covenant of redemption', Bavinck is keen to set out the trinitarian character of the doctrine,
The pact of salvation makes known to us the relationships and life of the three persons in the Divine Being as a covenantal life, a life of consummate self-consciousness and freedom. Here, within the Divine Being, the covenant flourishes to the full.... The greatest freedom and the most perfect agreement coincide. The work of salvation is an undertaking of three persons in which all cooperate and each performs a special task... It is the triune God alone, Father, Son and Holy Spirit, who together conceive, determine, carry out and complete the entire work of salvation. (Reformed Dogmatics Volume 3, p. 214-215).
The pact of salvation between the persons of the Trinity in eternity is the foundation of the saving acts of the triune God in the history of redemption.
All the grace that is extended to the creation after the fall comes to it from the Father, through the Son, in the Holy Spirit. The Son appeared immediately after the fall, as Mediator, as the second and final Adam who occupies the place of the first, restores what the latter corrupted and accomplishes what he failed to do. And the Holy Spirit immediately acted as the Paraclete, the one applying the salvation acquired by Christ. (RD. 3, p. 217).
And so it is that under both Old and New Testament dispensations that the Father saves his people by the redeeming work of the Son, applied to them by the Holy Spirit. "There is one faith, one Mediator, one way of salvation, and one covenant of grace." (RD. 3, p. 217).
Bavinck's treatment of the 'covenant of redemption' is thoroughly grounded in Scripture. He takes into account the trinitarian dimensions of the doctrine, relating the eternal pactum salutis between Father, Son and Holy Spirit to the historical fulfilment of the work of redemption. John Murray is not altogether happy in speaking of pre-temporal 'covenant' between the persons of the Trinity, preferring the designation 'inter-trinitarian economy of salvation.' (Collected Writings of John Murray, Volume 2, p. 130). But, as his suggested rewording implies, he is in full agreement with Bavinck's trinitarian emphasis,
The title ['inter-trinitarian economy of salvation'] is inclusive enough to comprise all aspects of the economy, eternal and temporal, pre-temporal design and fulfilment in time and in the ages to come... After all, our study of the plan of salvation will not produce abiding fruit unless the plan captivates our devotion to the triune God in the particularity of the grace which each person bestows in the economy of redemption, and in the particularity of the relationship constituted by the amazing grace of Father, Son and Holy Spirit. The fellowship of the living God is the fellowship of the Father, and of the Son, and of the Holy Spirit. (CW. 2, p. 131).
As set out by Bavinck and Murray (despite the latter's reservations concerning the use of covenant language when it comes to the pactum salutis), the 'covenant of redemption' demands a place in biblically faithful Reformed theology. In eternity and time salvation is of the Father, by the Son and through the Holy Spirit.