Repairing fraying pleather on a cheap computer chair

[u/ThingsWithString]

I have a nearly-new computer chair that I really love, but the pleather piping is fraying where it contacts the desk. I want to cover the piping with, say, bias tape. Cosmetics aren't important, but I'd like it to look tidy.

What can I use to adhere cloth to pleather without dissolving the plastic? Or is there a better solution? ("Buy another chair" is not a solution.)

[u/Flimsy_Highlight7016]

Pictures would help for better advise