J. I. Packer on the relationship of Holy Spirit and Jesus Christ, the incarnate Son:
The Spirit, whose creative power effected the conception of Jesus in Mary’s womb (Luke 1:35), was with and within the incarnate Son throughout his life on earth. He disclosed his presence to Jesus, to John, and perhaps to others by the apparition of the dove at Jesus’s baptism (Matt. 3:16-17; John 1:32-33), which convinced John that “this is he who baptizes with the Holy Spirit.” The Spirit bearer, so John was told, would in due course be the Spirit giver. The Spirit at once led Jesus into the wilderness “to be tempted by the devil” (Matt 4:1); he participated in all the Savior’s ministry (Luke 4:14), empowering his miracles (Matt 12:28), prompting his joy (Luke 10:21), and sustaining him through the agony of Gethsemane for the greater agony of his atoning death (Heb. 9:14). As we Christians are upheld by the Holy Spirit in the life that we live with God and for God, so was our Savior before us. As we live in a simultaneous relationship with the Father, the Son, and the Holy Spirit, who are always together and never apart from each other, so were the Father and the Spirit together with the Son when he was on earth, as they are still and always will be.
Quoting from Taking God Seriously: Vital Things We Need to Know 