Albert Barnes Commentary Romans 8:11

"But if the Spirit of him that raised up Jesus from the dead dwelleth in you, he that raised up Christ Jesus from the dead shall give life also to your mortal bodies through his Spirit that dwelleth in you." — Romans 8:11 (ASV)

But if the Spirit of him, etc. The Holy Spirit (Romans 8:9). He who raised up Christ, etc. He who had power to restore him to life has power to give life to you. He who did, in fact, restore him to life will also restore you. The argument here seems to be founded, first, on the power of God; and, secondly, on the connection between Christ and his people. Compare to John 14:19: Because I live, you shall live also.

Shall also quicken. Shall make alive.

Your mortal bodies. That this does not refer to the resurrection of the dead seems apparent, because that is not attributed to the Holy Spirit. I understand it as referring to the body, subject to carnal desires and propensities; by nature under the reign of death, and therefore mortal—i.e., subject to death.

The sense is that, under the gospel, by the influence of the Spirit, the entire man will be made alive in the service of God. Even the corrupt, carnal, and mortal body, so long under the dominion of sin, will be made alive and recovered to the service of God.

This will be done by the Spirit that dwells in us, because that Spirit has restored life to our souls, abides with us with his purifying influence, and because the design and tendency of his indwelling is to purify the entire man and restore all to God. Christians thus become sacred in their bodies and their spirits. For even their body, the seat of evil passions and desires, will become alive in the service of God.