Some further material from Kim, S.D. “Time and Eternity: A Study in Samuel Rutherford’s theology, with Reference to His Use of Scholastic Method,” Ph.D. diss., Aberdeen University, 2002.
“Rutherford fully develops the idea of ‘the covenant of redemption’ or ‘the covenant of Suretyship’ … Rutherford confirms there is ‘a covenant of Suretyship’ (or Redemption) between JEHOVAH and the Son of God’ in twelve arguments. It is worth summarizing the arguments in order to appreciate his points. He argues that there is a covenant of redemption because of Christ’s calling the Lord his God, because of the Lord’s way of calling Christ to his Office of Mediator, because of Christ’s voluntary offering of his service to God, because of the Father’s giving of the elect to Christ to be redeemed and the Son’s willingness of receiving, because of the receiving of the seals in order to prove Christ to be Surety of the covenant, because of the Lord’s liberty, because Christ was to be made the promise and the Covenant, because of the Lord’s promising that he shall be heard and prospered with success in his work, because of Christ’s working for wages and the Lord’s paying him his wage by a voluntary compact, because of the Oath of God by which Christ is made High Priest, because every priesthood is imposed by Covenant. Indeed, as may be observed, all that he elucidates concerning the covenant of Suretyship is saturated with teaching about Christ the God-Man and Mediator. Expressing the Christocentric emphasis in his theology, Rutherford writes that ‘Christ God-Man is in Covenant with God, being a person designed from eternity, with his own consent, and in time yielding thereunto, and yet he stands not in that covenant-relation that we stand in’.”
It is important to understand Rutherford’s reference to JEHOVAH here:
“According to Rutherford’s understanding, the Holy Spirit is included in the covenant of redemption. He says that there are two parties in the covenant of redemption; ‘Jehovah God as common to all the three on the one part, and on the other part is the only Son of God second person’, which is to say the three persons of the Godhead each take part in the covenant. When he describes the activity of God in the covenant of redemption, he prefers to use JEHOVAH rather than God or the Father.”
Durham does the same as well – the relationship of the Holy Spirit to the CoR in 17th C reformed thought could do with further study.