Pesters persistently (7)
I believe the answer is:
badgers
'pesters persistently' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for badgers that I've seen before include "Burrowing mammals with strong claws" , "Pesters; black and white nocturnal animals" , "Bullies" , "Pesters like burrowing animals" .)