Adam's failure to keep the stipulations of the CoW meant that the Holy Spirit withdrew from him and from the whole created order. If the Spirit is the Person of the Trinity that perfects all of God's external acts, this withdrawal seems to explain the Curse. In the CoG, the Holy Spirit restores this perfection in both man and the world, to be fully realized in glory.
It also appears that eschatological reward is the fullest reception of the Spirit that is possible. Adam forfeited this potential; but Christ, as the Last Adam, has received the Spirit without measure (John 3:34), and therefore, those united to Him shall enjoy perfection in the outward man even as they are now being perfected in the inward man.
"And thus Adam may be said to have had the Spirit of God in his innocency. He had him in these peculiar effects of his power and goodness; and he had him according to the tenor of that covenant whereby it was possible that he should utterly lose him, as accordingly it came to pass. He had him not by especial inhabitation, for the whole world was then the temple of God. In the covenant of grace, founded in the person and on the mediation of Christ, it is otherwise. On whomsoever the Spirit of God is bestowed for the renovation of the image of God in him, he abides with him forever. But in all men, from first to last, all goodness, righteousness, and truth, are the 'fruits of the Spirit,' Eph. v. 9." (John Owen, Pneumatologia)