It’s definitely good that you’ve got the little guy in a separate in-tank QT for now... that gives you some control over the situation while you figure out what’s going on, but you might want to go ahead and prep a proper QT tank if things take a turn for the worse.
If the injury was just from a run-in with rough rockwork, clean water and time should help - clownfish are pretty tough. If the other fish has been chasing it, that’s something to watch closely. Nine days in, new aggression is a bit unusual, but not impossible... sometimes it takes a little while for pecking order to establish, or one to realize it doesn’t like the other.
Personally, I think I'd keep them separate for now while you perhaps give the injured one Selcon - or something similar - with its food until it's looking healed and behaving a little more normally. Some people also recommend Vitamin C (use sodium ascorbate, not ascorbic acid) with food or directly to the tank - I'm not a reef chemist, so whether that's the right thing to do is over my paygrade - speaking for myself I'd probably try it, based on what I know. YMMV.
It’s certainly possible it could be something else, but nothing I can think of (for what that's worth) seems like a likely candidate based on your description. AFAIK most illnesses that cause fin damage wouldn’t take nine to ten full days to show up in a noticeable way. Bacterial infections can lead to fin rot, but that usually presents as fraying or slow deterioration, not a chunk suddenly missing overnight. Hitchhikers big enough this early on to take a chunk from a fish seem unlikely unless you used live rock that wasn't QT'd. The same goes for parasites - brooklynella and uronema are common concerns with clownfish, but they usually come with more obvious signs like rapid breathing, excess mucus, or a general lack of energy before any physical damage appears. If you start seeing anything like that, though, it’d be a reason to move to a full QT setup and potentially medicate. A photo under white light (not full blues, unless you’ve got a filter) could be really helpful to get a clearer look.
Since it sounds like the fish is already a little stressed, keeping the lights low for a few days should help while you keep them separate and do what you can to nurse it back to health. When you’re ready to reintroduce it back into the main tank, doing it when the lights are off can give it a chance to settle in without as much risk of the other fish getting territorial. Let the lights stay off for a full day at least, then bring them back up gradually over the course of a week.
For now, just keep a close eye on the injured guy, and assuming he recovers, the both of them when you re-introduce... if the aggression doesn’t stop, you might need to intervene again and possibly re-home one of them. And if anything starts looking worse, or you notice other symptoms popping up, be ready to stand up a proper QT tank with a quickness, just in case.
