What do the Scriptures teach as to the activities of the Holy Spirit in the eternal state, especially in relation to the individual believer?
The sum total of Scripture teaching as to the eternal state is very small. Scripture is, for the most part, occupied with time, men, and Christ in relation to the earth and men. It tells but little of a past eternity or a future. The chief doctrine of the Holy Spirit has to do with His residence on earth maintaining the interests of Christ here during His absence. There are, of course, certain things which are eternally true of the saints and which things must, therefore, be carried on into the eternal state, e.g., their vital link with a risen Christ is effected by the Spirit’s dwelling within: that can never cease. Again, they are sealed with the Holy Spirit unto the day of redemption, but that seal does not, of course, cease then. As the inter-relations of the Godhead remain eternally unchanged so, too, does the work of the Spirit in regard to the believer remain unchanged, save only that with the passing away of time and earth the need for certain of His operations also passes. Similarly His presence on earth is a demonstration to the world of sin, righteousness and judgment, but when the eternal state arrives sinners will have been judged and the need for that demonstration will no longer exist.
Consequently, there are certain functions of the Spirit of God which are temporary. There are others which are eternal. It is a fact of no small importance that after the resurrection of the Lord Jesus it was by the Spirit He gave commandment to His apostles. There was thus perfect co-operation of the Son and the Spirit in the resurrection state. There is no hint that this will ever cease.