ANY FIX FOR CRACKING PAINT (previous owners cheap paint PIC)

The only right way to fix your problem is to get the bumper repainted. Who ever painted the bumper did not prep it right. The only other is to sand the peeling paint back a little bit with some 320 grit sandpaper. Then run some masking tape right on the sharp edge of the bumper right below the lights. Take either black or the colormatch spray paint and paint the top ledge under the lights. It will look beter than what you have now