Here’s some classic Edward Fisher from the Marrow of Modern Divinity on the work of Christ for the elect:
[It is] as if God [the Father] had said concerning his elect, I know that these will break, and never be able to satisfy me; but thou [God the Son] art a mighty and substantial person, able to pay me, therefore I will look for my debt of thee. As Pareus well observes, God did, as it were, say to Christ, What they owe me I require all at thy hands.
Then said Christ, “Lo, I come to do thy will! in the volume of the book it is written of me, I delight to do thy will, O my God! yea, thy law is in my heart,” (Psa 40:7,8). Thus Christ assented, and from everlasting struck hands with God, to put upon him man’s person, and to take upon him his name, and to enter in his stead in obeying his Father, and to do all for man that he should require, and to yield in man’s flesh the price of the satisfaction of the just judgement of God, and, in the same flesh, to suffer the punishment that man had deserved; and this he undertook under the penalty that lay upon man to have undergone. And thus was justice satisfied, and mercy by the Lord Jesus Christ; and so God took Christ’s single bond; whence Christ is not only called the “surety of the covenant for us,” (Heb 7:22), but the covenant itself, (Isa 49:8). And God laid all upon him, that he might be sure of satisfaction; protesting that he would not deal with us, nor so much as expect any payment from us; such was his grace.