Nuisance to turn out pets (4)
I believe the answer is:
pest
'nuisance' is the definition.
(I've seen this before)
'turn out pets' is the wordplay.
'turn out' is an anagram indicator.
'pets' anagrammed gives 'PEST'.
'to' acts as a link.
(Other definitions for pest that I've seen before include "Plague" , "Infernal nuisance" , "Aphis" , "Annoying creature" , "Destructive insect or nuisance" .)