What color is your car?
Also, clear coat is just clear paint. I had a small area of my car (the bottom of the passenger side windshield pillar) painted and clear coated after the dealer put several small scratches on it that penetrated to the primer. Visually and by touch you wouldn't know it was there. So it can be done.
If only the clear coat has scratches, you should first rub it out.
I use white polishing compound by No.7 to remove heavy scratches/swirls.
Some of the detailers/painter use 1200 or 1500 grit sand paper for stuff like this.
Check the detailing forum for more info and techniques of scratch removal
Start out with the light stuff and proceed with the heavier compounds until you see results.
2004 E60 530is, Delivered 12/12/03, TiSilver/LGrey, PP, SP,PS, PDC, ACC, FRS, Step, Xenons, clear bra, body colored rear inserts. (Retired, 1983 henna red 320is)
2004 Corvette Z06 Commemorative Edition