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