Some say that the Holy Spirit is celebrated on the Day of Pentecost, and that the following Monday is the feast of the Holy Trinity.
But let’s not confuse the liturgical order, which is clear.
The mystery of the Holy Trinity is revealed on both days, first and foremost on Sunday, which is the day of the Feast, and then on Monday we have the Synaxis of the Holy Spirit.
Monday is the Synaxis of the Holy Spirit. On the Synaxis of a feast we celebrate the “agent” of the feast in question (of the saving event), which in this case is God the Holy Spirit.
Indeed, the whole week following the Feast of Pentecost is referred to as the Week of the Holy Spirit.
For further information, take a look at "On How the Holy Spirit was Manifested and Shared Out at Pentecost", Homily 24, Saint Gregory Palamas: The Homilies.
When God the Holy Spirit as the Third Member of the Holy Trinity is revealed, as a Person (and not merely as a power of God), of course the Holy Trinity is revealed; which, by the way, is clearly present in the Old Testament as well as in the New Testament: Elohim (God), Yahweh (I AM), Ruach (Spirit).
The role of the Holy Spirit - the Conforter and Spirit of Truth - is to reveal Christ to us (Who is the Truth) as both our Creator, our God, and our Saviour.
For further information, take a look at "On How the Holy Spirit was Manifested and Shared Out at Pentecost", Homily 24, Saint Gregory Palamas: The Homilies.
DrCNV