In 1 Corinthians 13:14 Paul writes, The grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Spirit, be with you all. Amen.
These words of Paul are often used to help make a case in support of trinitarian doctrine, but I don’t think this is Paul’s intent here. Instead, the communion of the Holy Spirit seems to be a reference to fellowship among believers because of the love of God and grace of Christ. Only two short verses prior to this statement Paul writes, “greet one another with a holy kiss.”
Paul’s teachings are filled with exhortations of unity among believers as the household of God.
In Ephesians 4, Paul tells the church at Ephesus to walk worthy of the vocation wherewith ye are called, With all lowliness and meekness, with longsuffering, forbearing one another in love; endeavouring to keep the unity of the Spirit in the bond of peace. ~ Ephesians 4:1-3
Paul then says, There is one body, and one Spirit, even as ye are called in one hope of your calling… ~ v. 4.
Paul’s doctrine regarding the Holy Spirit has far more to do with Christ in us, and the unity of the saints than attempting to prove the triune nature of the Godhead. Consider for example, Paul’s words in Ephesians 2.
For through him (through Jesus) we both (Jews and Gentiles) have access by one Spirit unto the Father. Now therefore ye (Gentiles) are no more strangers and foreigners, but fellow citizens with the saints, and of the household of God; And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone; In whom all the building fitly framed together groweth unto an holy temple in the Lord: In whom ye also are builded together for an habitation of God through the Spirit. ~ Ephesians 2: 18-22
Paul is the only writer in all of scripture that gives us the concept that believers are corporately the body of Christ and the temple of God’s Holy Spirit. There are references to unity elsewhere in the New Testament but only Paul expounds on the church as the body of Christ in-dwelt by the Spirit of God.