Pets turn out to be vermin (4)
I believe the answer is:
pest
'to be vermin' is the definition.
'pets turn' is the wordplay.
'turn' is an anagram indicator.
'pets' is an anagram of 'PEST'.
'out' is the link.
(Other definitions for pest that I've seen before include "Destructive insect or other animal" , "Troublesome man or animal" , "Menace" , "Troublesome person" , "Nuisance; half a European capital" .)