What sort of problems can be caused by chipped insulation on an axial resistor? I'm not seeing a problem, but I wonder.
If it is only chipped insulation the answer is probably "none". If the ceramic body has been cracked by whatever blow caused the insulation to crack then the part may already be a higher resistance than it should be and may fail totally at a later date.
If the part is easy to replace then I'd recommend just replacing it. If that's difficult then I'd examine it carefully under good magnification to try to determine the extent of the damage.
It was chipped when I removed a nearby jumper that was glued/epoxied also to the resistor. It's difficult to see if the resistor core is exposed or not, and difficult to access.
But just as a general question, what's the function of the insulation? Prevent accidental shorts, arcing, protect core deteriorating from environment?
Just dab some nail polish on the broken component.
Check its value, if it's out of tolerance then replace it.