The way the Spirit subsists in God shows up in the way the Holy Spirit carries out the divine works of redemption. Just as he is third, or we might say final, in the eternal order of perfect deity, he behaves thirdly or finally in the work of God. “To him belongs by economic office the consummation of things.”
Petrus van Mastricht’s Theoretical-Practical Theology (volume 2, chapter 27) has an excellent treatment of the Holy Spirit. I just want to unpack a little something he says in the introductory paragraph, before he gets to the main body of the pneumatology (in parts exegetical, dogmatic, elenctic, and practical). Here’s a little picture of the Latin, just to remind us all how grateful we should be to live in an age when the English translations are finally emerging.
Mastricht says that we affirm the Spirit “has the third place” for two related reasons. First, In “the order and mode of subsisting,” he subsists from the Father and the Son. Second, in the “mode of operating,” he operates from the Father and the Son. What this shows is that “just as he subsists, he also operates” (sicut subsistit, ita etiam operatur).
So we start at the highest level of trinitarian affirmation: The Holy Spirit is God, but is a particular person or hypostasis of God. That personal existence, or subsistence, is in God in a particular, relational way: eternally from the Father and the Son. Subsisting in that way, as third, he also operates in that way. But here’s the tricky bit: when Mastricht says “operate,” he is not yet talking about an outward work of the Trinity. It’s not an operation in that sense yet. Because “operation” can also refer to an inward, eternal operation. That inward operation is of course something we already know about: it follows the order of subsistence, meaning it aligns with the eternal relation of proceeding from the Father and the Son. All of this (origin, subsistence, operation) at the level of the eternal, internal, essential life of the triune God.