We do pray to the Holy Spirit when we pray to God. A prayer to the Triune God is a prayer to the Holy Spirit.
Can we address a prayer specifically to the Holy Spirit? Certainly. For example, we do that in our churches on Pentecost Sunday. This is the Prayer of the Day for that festival: “Holy Spirit, God and Lord, come to us this joyful day with your sevenfold gift of grace. Rekindle in our hearts the holy fire of your love that in a true and living faith we may tell abroad the glory of our Savior, Jesus Christ, who lives and reigns with you and the Father, one God, now and forever. Amen.”
Romans 8:26-27 teaches that the Holy Spirit is very much involved in our prayer life. Along with the Father and the Son, the Holy Spirit hears and answers our prayers in wisdom and love.