Kitty will act up (3)
I believe the answer is:
cat
'kitty' is the definition.
(thesaurus)
'act up' is the wordplay.
'up' indicates an anagram.
'act' is an anagram of 'CAT'.
'will' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for cat that I've seen before include "Carnivore; whip" , "See 23" , "Pussy" , "Feline mammal" , "one's pyjamas? They're an excellent thing" .)