Dog — a figure following cat, initially (6)
I believe the answer is:
canine
'dog' is the definition.
(thesaurus)
'a figure following cat initially' is the wordplay.
'figure' becomes 'nine' (I've seen this in other clues**).
'following' means one lot of letters go next to another.
'initially' suggests taking the first letters.
The first letter of 'cat' is 'c'.
'a'+'nine'='anine'
'anine' put after 'c' is 'CANINE'.
(Other definitions for canine that I've seen before include "Pointed conical tooth" , "Of or like dogs" , "A tooth; of our best friend" , "such as Lassie" , "Dog-like" .)