A clear coat has mainly its purpose to protect the underlying surface (the carbon/resin laminate) against scratches and UV.

I'm not sure if that's your only objection. Or is it aesthetically too?

What new clear coat you want to apply? If it's PU based only roughing up the underlying base with light sanding will do the job.
It's clear that if you should change to a coloured finishing coat instead of a clear one, you have the least problems.

You then have to sacrifice the carbon-look though