The obedience of faith may be one of the most underrated and underused expressions in the Scriptures. It’s only used twice, once in Paul’s greeting to the Romans (Romans 1:5) and again in the benediction of Romans (Romans 16:26), but we should use it more often.
There are a couple proposed interpretations for the phrase.
One possibility is that πίστεως (“of faith”) is a genitive of apposition, where the genitive restates the same idea as in the main noun, or what’s sometimes called an epexegetical genitive, where the genitive clarifies the meaning of the head noun. If that’s the case, the Paul’s mission was to bring about “obedience, that is, faith,” so that obedience is a larger category of which faith is a more specific kind. That interpretation could work. It’s at least theologically correct, and could be compared to John 6:29 where Jesus called faith a work of God (to be done). And since “believe” is an imperative (Mark 1:15), faith would be obedience to the command.
But πίστεως seems to me to better fit the pattern of the genitive of source (or genitive of production). Pauls’ mission was to bring about “obedience derived from or sourced in faith,” or even with the gloss, “obedience produced by faith.”
When I think about the flow of the letter, with the emphasis on justification by faith followed by Paul’s immediate response to anticipated arguments about faith and grace denying the obligations of obedience, especially in chapters 5 and 6, it causes me to lean toward the interpretation of the (necessary) obedience that comes from faith.
I also take Paul’s quote from Habakkuk about the righteous living by faith (Habakkuk 2:4 in Romans 1:17) to refer to faith-driven righteous behavior, not just faith-received justification, though it has to start there.
The Great Commission requires that disciples be taught to “observe all that (Jesus) commanded” (Matthew 28:19). This means that complete obedience to the Lord is the mission, though we understand such a life starts with faith in Him.
We are forgiven by grace alone through faith alone, and then re-formed, still by grace through faith. But this re-formed obedience is a post-requisite. We are being transformed (Romans 12:1), we are being conformed to the image of His Son (Romans 8:29). This is sanctification. Our resurrection in Christ causes us to “walk in newness of life” (Romans 6:4), and sometimes we need to have the feet of our hearts washed again (see John 13:10). The whole thing is from faith to faith (Romans 1:17), and obedience is the fruit of healthy faith.
Faith is no more an enemy of works than the sun is an enemy to flowers. Obedience is the bloom, the color, the fragrance of salvation in the flesh. It is the obedience of faith.