Likely a damage from Oriental Fruit moths, serious pest for peaches, plums and other fruit.

Google Oriental Fruit Moth Fact Sheet. It will give you info you need. You can eat fruit. Cut off damaged part. Watch out for larvae inside.

Plum is not easy to grow. OFM is only one of several issues plums encounter. It depends on where you are located. In a drier area, it has less fungal and bacterial diseases. Otherwise, watch out for canker, rot and black knot, too.