Badgered wild deer, pursuing vermin (8)
I believe the answer is:
pestered
'badgered' is the definition.
('pester' can be a synonym of 'badger')
'wild deer pursuing vermin' is the wordplay.
'wild' is an anagram indicator.
'pursuing' is a charade indicator (letters next to each other).
'vermin' becomes 'pest'.
'deer' is an anagram of 'ered'.
'ered' after 'pest' is 'PESTERED'.
(Other definitions for pestered that I've seen before include "Harassed, annoyed" , "Annoyed persistently" , "Annoyed with frequent questions or requests" , "Constantly bothered by deer pets" , "Constantly irritated by deer pets" .)