The Holy Spirit, unless you’re a Pentecostal or Charismatic, is often left in the background somewhere in theological discussion. Never mind that John Calvin has been called the ‘theologian of the Spirit’ or the fact that Colin Gunton made great appeal to the Spirit in his doctrine of creation, or that folks like my friend and Evangelical Calvinist colleague, has edited books devoted to Third Article Theology; the Spirit, in my experience anyway, is often under-referenced in the Reformed circles I have contact with when discussing things theological. And maybe some of this is actually by design: I mean the Holy Spirit’s ministry is to magnify the person and work of Jesus Christ; so He, by His person (hypostasis) stands in the background. As T Torrance was fond of highlighting, the Holy Spirit comes along for us with the coming of the eternal Son in the Incarnation; in other words, the Spirit comes with the Son for us, indeed he paves the way (think of the overshadowing of the waters in Genesis [protology – creation] or the overshadowing of Mary’s womb in Luke [eschatology – recreation]).
The aforementioned noted, the Holy Spirit was given his rightful place in the development of the Trinitarian theology that took was given expression in the Niceno-Constantinopolitan Creed of 381. Kooi and Brink highlight this especially well when they write:
The question might be posed as to why, between 325 and 381, the view arose to describe the Spirit too as being of one essence (“consubstantial”) with the Father and the Son. Was that not a little too much of a good thing? Was a binitarian concept that safeguarded Jesus’s divinity not complicated enough? It was precisely in the fourth-century controversy with those who doubted the divinity of the Spirit that it became clear that the Trinitarian concept was not to be relinquished. It was not based just on some Bible texts that linked the Spirit to God; it had much more to do with the pneumatological insight developing in the early church that we human beings do not have the Spirit at our disposal and that we cannot manipulate the Spirit. A spirit that does not issue from God would automatically be on the side of the creatures and open to such manipulation. Nor would such a spirit be able to genuinely connect us with God. We would be left out on our own. Only because the Spirit is radically on God’s side is he able, through the Son, to incorporate us into communion with the Father. However, this work can happen only if the Spirit belongs fully, as a distinct person, to the divine essence. This soteriological insight played a major role in the labors of Athanasius and the Cappadocians and would eventually lead to the confession that the Spirit “is Lord and gives life” and must “be worshiped and glorified together with the Father and the Son” (the Niceno-Constantinopolitan Creed of 381, an expansion of the Nicene Creed; hereafter we will refer to both forms simply as the Nicene Creed).
I like how they highlight that the Holy Spirit indeed is God of God; i.e. that He is indeed a hypostasis within the Godhead (Monarxia), and as such is Lord (cf. II Cor. 3.17). He is not an energy or a spark within humanity, He finds His reality in the eternal relation and coinhering life of the Father, Son, and indeed, the Holy Spirit.
 Cornelius van der Kooi and Gijsbert van den Brink, Christian Dogmatics: An Introduction (Grand Rapids, Michigan: William B. Eerdmans Publishing Company, 2017), 94-5.