Annoy the burrower persistently? (6)
I believe the answer is:
badger
'annoy the burrower persistently?' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for badger that I've seen before include "Beast blamed for TB" , "Animal hunted by stocky dog" , "Carnivore - pester" , "Harass - brock" , "Pester the burrowing animal" .)