Pet will act up (3)
I believe the answer is:
cat
'pet' is the definition.
(cats are often kept as pets)
'act up' is the wordplay.
'up' indicates anagramming the letters (letters get chucked up).
'act' with letters rearranged gives 'CAT'.
'will' is the link.
(Other definitions for cat that I've seen before include "Carnivore; whip" , "A tom" , "Domestic animal" , "Animal; converter; boat" , "Pussy" .)