You need a new handle and lock mechanism, both fairly cheap ( just replaced two of mine at about £20 for the pair ).Unscrew the handle and remove the lock, then you could glue a strip of uvpc trim over the area to repair ( redrill hole to accommodate lock spindle and screw holes) when buying a handle get one with a cam which is slightly longer than existing to pass thru the extra depth of the repair .
You may have to trim a longer cam to size if you can’t get a close match .