Pet is displaying ill will (5)
I believe the answer is:
spite
'ill will' is the definition.
(I've seen this in another clue)
'pet is displaying' is the wordplay.
'displaying' indicates an anagram (the anagrammed letters display the answer).
'pet'+'is'='petis'
'petis' is an anagram of 'SPITE'.
(Other definitions for spite that I've seen before include "Hatred" , "Venom" , "Desire to intentionally and maliciously hurt or offend" , "Malicious desire to hurt or humiliate" , "Bitchiness or malice" .)