You should have clearcoated your carbon fiber parts, or they may have come clearcoated. Either way, this needs to be done. This is very important because of the UV protection. I always ask for something with UV additives in it, but I don't know what's good and what's not. I just make carbon stuff, I leave the paint work to the more skilled people.
Once you have it clearcoated, take care of it just like the rest of your paint. Trust me, it will last longer, not chalk out, and if you're lucky, it won't turn yellow. The yellow part won't necessarily be your fault though, if it's made with crap resin it will turn yellow no matter what.
Anyway, get that shit clearcoated!