Nibble persistently (4)
I believe the answer is:
gnaw
'nibble persistently' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for gnaw that I've seen before include "Chew persistently at, say a bone" , "What rodents typically do" , "Nibble like a rodent" , "Eat at" , "Chew at, work with teeth" .)