(Jesus' role of mediator comes from a covenantal agreement within the Godhead)
Edwards saw the Trinity as three persons with distinct roles that are voluntarily undertaken and not distinguishable in amounts of glory. Within the Trinity, says Edwards, is an agreement, a pactum salutis, where the Father is the one who sends the redeemer, who is the Son, the one who mediates. The Holy Spirit is the one who is the source of and endpoint of this redemptive agreement within the Trinity. Edwards' asserts an ordering within the Trinity and he doesn't see an interchangeability of roles.
Since God's purpose is to display and communicate his glory to his creatures , he makes them loveable through the redemptive work of Christ. “In other words, God makes unlovable loveable that He may communicate to them His happiness. … He was moved by no merit in the creature.” (Infinite Merit, Bheil, 69) Christ is a mediator able to stand in God's place “to transact with man, and in man's place to transact with God.” (71) Edwards writes; “Man's law required the obedience of that nature, an obedience performed with the strength and under the circumstances and imperfections of that nature and the temptations that it is liable to. It was therefore essential that Christ should be in the same nature, because the law could not be properly answered.” (79)
As the incarnate mediator Jesus is subject to the Jewish Law but also still a person of the Godhead, and as such unlike any creature, a participant in God's redemptive purposes. The Holy Spirit “is the happiness of God to be eternally communicated to the church.” (82)