Domestic animal (3)
(Other definitions for cat that I've seen before include "one's pyjamas? They're an excellent thing" , "Pussy" , "Tiger, for instance" , "Grimalkin" , "Malicious gossip" .)
'domestic animal' is the definition.
(animal kept in the home)
This is the entire clue.
(Other definitions for pet that I've seen before include "Little darling" , "Favourite, darling" , "Paddy" , "Domesticated animal" , "Preferred" .)