Pets turn out to be a blight (4)
I believe the answer is:
pest
'a blight' is the definition.
(thesaurus)
'pets turn out' is the wordplay.
'turn out' indicates anagramming the letters.
'pets' is an anagram of 'PEST'.
'to be' acts as a link.
(Other definitions for pest that I've seen before include "Destructive insect or nuisance" , "Annoying creature" , "Nuisance; half a European capital" , "Destructive creature" , "A nuisance - step on it" .)