While we might often think of prayer to Jesus or God the Father as "separate" from the Holy Spirit, the truth is that whenever we pray, the Holy Spirit is there.
The Catechism of the Catholic Church explains this mystery in its section on prayer:
"No one can say 'Jesus is Lord' except by the Holy Spirit." Every time we begin to pray to Jesus it is the Holy Spirit who draws us on the way of prayer by his prevenient grace. Since he teaches us to pray by recalling Christ, how could we not pray to the Spirit too?
The Holy Spirit often works mysteriously in our lives, always present, but not always in the front of our mind.
One way we can recognize the work of the Holy Spirit in our prayer lives is to openly invoke the Holy Spirit in all things:
That is why the Church invites us to call upon the Holy Spirit every day, especially at the beginning and the end of every important action.
The next time you prayer, recall the action of the Holy Spirit and how every prayer is Trinitarian.