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clay wont do the job. You'd have to sand it down prior to trying to re-apply the clear, but I'm pretty sure that any painter wouldn't recommend just trying to re-apply clear. To do it right, you'd have to re-spray the color too.
Ok.. What could have caused this? Just normal wear and tear? or something else?
My guess is that someone backed into your bumper. There may also be an issue with the type of clear coat on your bumper. The bumper uses a clear that is more elastic than that used on the metal. If your car was repaired at one time and they sprayed the wrong clear it could react like that. As I look at the damage though, it looks like your bumper was hit.
The clear coat might not have been mixed with a flex additive when painted. This allows for the paint to give a little bit as the bumpers are bendable parts. If it was not added, the clear coat would be very brittle and any stretching or flexing would cause the spider web effect, and eventually lead to cracking and chipping off.
Do you know if you are the first owner. People do body work to their cars outside of insurance claims.
Regardless of what the cause is, to fix this problem will require the old clear coat being stripped off and a new base coat/clear coat applied.