Albert Barnes Commentary Romans 8:4

"that the ordinance of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit." — Romans 8:4 (ASV)

That the righteousness of the law. That we might be conformed to the law, or be obedient to its requirements, and no longer under the influence of the flesh and its corrupt desires.

Might be fulfilled. That we might be obedient, or comply with its demands.

Who walk. See the notes on Romans 8:1.