Rather than attempting a theological formulation, I will seek a solution from devotion, which I believe can clue us in to how the cross and the Spirit interact within a single exercise of faith. I have found in my experience that the Spirit confirms faith in the cross. To elaborate, when I engage with the cross by faith and repentance, trusting in the forgiveness of sins and gift of righteousness provided in Christ’s redemptive work, then the Spirit acts in that instance to confirm that the gospel I am believing in is indeed true and efficacious for my salvation. Put another way, the gift of the Spirit is God's “yes” to my repentance and faith in Christ. Through inner conviction, joy and peace, freedom from sin and oppression, miracles, and other means, the Spirit seals our faith and authenticates the good news about Jesus.
This dynamic between faith in Christ’s work on the cross and the Holy Spirit can be repeatedly seen in Acts, where new believers are filled with the Holy Spirit upon receiving the apostles’ proclamation of forgiveness and salvation in Jesus. Testimonies of conversion in general seem to follow this pattern. Repentance and faith in Jesus are typically accompanied by experiences of joy, freedom, and new life, without which conversion does not seem complete. Moreover, this interaction between faith and the Spirit continues after conversion. Paul makes this point when he questions the Galatians: “Did you receive the Spirit by works of the law or by hearing with faith? Are you so foolish? Having begun by the Spirit, are you now being perfected by the flesh? . . . Does he who supplies the Spirit to you and works miracles among you do so by works of the law, or by hearing with faith?” (Gal 3:2-5). The activity of the Spirit remains contingent on faith in the gospel throughout the course of one’s discipleship.
Within this scheme, the Spirit seems ancillary to the cross. I am inclined to think so. I concur with Paul that “of first importance” is Christ’s death for our sins and his resurrection (1 Cor 15:3-4). However, that does not make the Spirit any less necessary or important, for he is given to confirm and solidify trust in Jesus’ saving work. This is the context for the activity of the Spirit, which is crucial as there have been many cases of misapplying the gifts of the Spirit for purposes tangential or even contrary to the way of the cross. Conversely, there are some who employ the language and forms associated with the cross but have not the life and power of the Spirit and thus would do well to consider if they are encountering the cross of Christ at all.