So, there was an incident and now one of the mats has a hole in it. The hole is about 1 x 0.5 cm wide. What is the best way to repair it so it is still safe to train on said mat?
The mat is a plastic covered foamed judo mat similar to this one.
That doesn't sound like a huge hole. I would at least consider taping it and moving it to the to a spot off to the side.
If that solution sets off your safety or insurance alarms, I'd look into a mat repair kit. The Swain one includes:
Wrestling mats have a different set of recommended patch kits.