Nibble at (4)
I believe the answer is:
gnaw
'nibble at' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for gnaw that I've seen before include "Bite and wear away" , "Wear away with the teeth" , "Chew upon" , "Bite persistently, grind" , "Prey on one's mind" .)