The river flowing from the Throne of God is a figure of the Holy Spirit, but by the waters spoken of by David the powers of heaven are intended. The kingdom of God is the work of the Spirit; and it is no matter for wonder if He reigns in this together with the Son, since St. Paul promises that we too shall reign with the Son.
153. And this, again, is not a trivial matter that we read that a river goes forth from the throne of God. For you read the words of the Evangelist John to this purport: “And He showed me a river of living water, bright as crystal, proceeding out of the throne of God and of the Lamb. In the midst of the street thereof, and on either side, was the tree of life, bearing twelve kinds of fruits, yielding its fruit every month, and the leaves of the tree were for the healing of all nations.”
154. This is certainly the River proceeding from the throne of God, that is, the Holy Spirit, Whom he drinks who believes in Christ, as He Himself says: “If any man thirst, let him come to Me and drink. He that believes in Me, as says the Scripture, out of his belly shall flow rivers of living water. But this spoke He of the Spirit.” Therefore the river is the Spirit.
155. This, then, is in the throne of God, for the water washes not the throne of God. Then, whatever you may understand by that water, David said not that it was above the throne of God, but above the heavens, for it is written: “Let the waters which are above the heavens praise the Name of the Lord.” Let them praise, he says, not let it praise. For if he had intended us to understand the element of water, he would certainly have said, Let it praise, but by using the plural he intended the Powers to be understood.
156. And what wonder is it if the Holy Spirit is in the throne of God, since the kingdom of God itself is the work of the Holy Spirit, as it is written: “For the kingdom of God is not meat and drink, but righteousness and peace and joy in the Holy Spirit.” And when the Saviour Himself says, “Every kingdom divided against itself shall be destroyed,” by adding afterwards, “But if I, by the Spirit of God, cast out devils, without doubt the kingdom of God has come upon you,” He shows that the kingdom of God is held undivided by Himself and by the Spirit.
157. But what is more foolish than for any one to deny that the Holy Spirit reigns together with Christ when the Apostle says that even we shall reign together with Christ in the kingdom of Christ: “If we are dead with Him, we shall also live with Him; if we endure, we shall also reign with Him.” But we by adoption, He by power; we by grace, He by nature.
158. The Holy Spirit, therefore, shares in the kingdom with the Father and the Son, and He is of one nature with Them, of one Lordship, and also of one power.
Source: On the Holy Spirit (New Advent)