Witch Hunters Zealots special rule

I would presume the first round attacking a new foe. So if you charge unit A, you get +1 attack in the first round against unit A. Next round you're still fighting unit A so you don't get a bonus attack.

Later on you charge unit B. This is a new enemy so this is your first round of combat against them. Unit B flees and somehow escapes (I'm not sure that's possible unless you're hemmed in by a unit C). Later you charge unit B again. This is the beginning of a new fight against them so you get it again.

Now you're fighting unit C. Unit D comes and joins in. Technically this starts a new fight with unit D but you're still fighting unit C. If you attack unit C you get no bonus attacks. If you attack unit D some might argue you get the bonus attack but you're already in a fight so I'd say no personally (it's simpler that way). After you kill unit C you are not beginning a new fight against unit D since you've already been fighting them so no bonus attacks there either.

Having it just be for your first batch of attacks against them every turn seems dumb. Having it be every round instead of every turn also seems almost as dumb but is probably done for simplicity's sake rather than for logic. It's unfortunate that they refer to rounds of combat as rounds of combat because it could be confused with an actual round (each player taking one full turn).