to pursue: to chase hard after someone or something, whether to harm them, to overtake them, or to reach a goal
At its root this word pictures running hard after a target. That single image of relentless pursuit branches into the ways the New Testament uses it, and the branches share more than they first appear to.
Most often the target is a person, and the pursuit is hostile: to hunt down, harass, and harm. This is the standard word for persecuting believers, and it is what the risen Jesus means when he asks Saul, "why are you pursuing me?" But the same energy can be aimed at a good end. Writers turn the word into a vivid command to chase after love, peace, righteousness, and the prize ahead, the way a runner strains toward the finish line. The pursuit is just as intense; only the object has changed.
Readers should not flatten these into one English word. The chase that means "hound and harm" and the chase that means "strive eagerly for" are the same verb wearing two faces, and the writers sometimes play on that. Paul, who once pursued the church to destroy it, now describes himself pursuing Christ with the same wholeheartedness, and the echo is deliberate.