Story about an animal: a dog (6)
I believe the answer is:
lassie
'a dog' is the definition.
(I've seen this before)
'story about an animal' is the wordplay.
'story' becomes 'lie' (I've seen this before).
'about' is an insertion indicator.
'an animal' becomes 'ass' (I've seen this before**).
'lie' going around 'ass' is 'LASSIE'.
(Other definitions for lassie that I've seen before include "Young Scottish girl or Hollywood lost dog" , "Collie featuring in many films" , "Cinema dog who went home" , "TV/film dog" , "Hollywood film-star dog" .)