The Holy Spirit quickens the mortal body of the believer. It is very evident from the context that this refers to the future resurrection of the body (vs.21-23). The resurrection of the body is the Holy Spirit's work. The glorified body is from Him; it is "a spiritual body." At the present time, we have only the first fruits of the Spirit and are waiting for the full harvest, the redemption of our body (v.23).
There is, however, a sense in which the Holy Spirit even now quickens our bodies. Jesus tells us in Matt. xii.28 that He cast out devils by the Spirit of God. And we read in Acts x.38, "How God anointed Jesus of Nazareth with the Holy Ghost and with power, who went about doing good and healing all that were oppressed of the devil." In James v.14, the Apostle writes, "Is any sick among you? Let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord." The oil in this passage (as elsewhere) is the type of the Holy Spirit, and the truth is set forth that the healing is the Holy Spirit's work. God by His Holy Spirit does impart new health and vigour to these mortal bodies in the present life. To go to the extremes that many do and take the ground that the believer who is walking in fellowship with Christ need never be ill is to go farther than the Bible warrants us in going. It is true that the redemption of our bodies is secured by the atoning work of Christ but until the Lord comes, we only enjoy the first fruits of that redemption; and we are waiting and sometimes groaning for our full place as sons manifested in the redemption of our body (Rom. viii.23). But while this is true, it is the clear teaching of Scripture and a matter of personal experience on the part of thousands that the life of the Holy Spirit does sweep through these bodies of ours in moments of weakness and of pain and sickness, imparting new health to them, delivering from pain and filling them with abounding life. It is our privilege to know the quickening touch of the Holy Spirit in these bodies as well as in our minds and affections and will. It would be a great day for the Church and for the glory of Jesus Christ, if Christians would renounce forever all the devil's counterfeits of the Holy Spirit's work, Christian Science, Mental Healing, Emmanuelism, Hypnotism and the various other forms of occultism and depend upon God by the power of His Holy Spirit to work that in these bodies of ours which He in His unerring wisdom sees that we most need.