It's normal for leather corals to reproduce by splitting a piece off their crown or their branches and dropping it free. The edges where the split occurs is usually white and smooth, and heals after a few weeks.
Your edge looks fuzzy. Is it only fuzzy in that one spot? If so, I would give it a week and see what happens. If the coral appears to be declining rapidly in that one spot, I would assume infection or something localized and cut off that section. Take sharp scissors and make a cut about an inch below the fuzzy area. Leathers are very tolerant to fragging this way.
Do you have fish like angels that might nip at soft corals? Even if you've had a fish in the tank for a long time, one day it might taste the leather and go mmm.
Does the coral ever have good polyp extension on it's other branches? If the whole coral is always retracted, something is irritating it. Too high of lighting, especially with LEDs, is always the first thing I check. Is the leather a new addition? If so, it's probably getting too much light and should be moved lower. Have you adjusted or changed your LEDs lately.
Is there a coral within 12" that has long night-time sweepers like galaxia, euphyllia, or pectinia? I doubt it would cause this sort of damage, but it's worth checking. Their nighttime sweeper tentacles are amazingly long.
Too much flow is the next thing I would check. Then, something major with your water quality like ammonia.
While there are parasitic nudibranchs that eat leather corals, IME they're not that common and I don't think that's the problem here. You'll find their egg masses out of sight on the coral's main branch, or underneath the crown if it has one. Look for a dime-sized spiral of eggs.
