Your third pet's terribly distressed (5)
I believe the answer is:
upset
'distressed' is the definition.
(I've seen this before)
'your third pet's terribly' is the wordplay.
'your third' becomes 'u' (3rd letter of 'your').
'terribly' indicates an anagram.
'pets' with letters rearranged gives 'pset'.
'u'+'pset'='UPSET'
(Other definitions for upset that I've seen before include "Trouble" , "Distressed - unexpected defeat" , "Make unhappy; disrupt" , "Knocked over; unhappy" , "Sad" .)