Girl’s story involving donkey (6)
I believe the answer is:
lassie
'girl's' is the definition.
(lassie can informally mean a girl)
'story involving donkey' is the wordplay.
'story' becomes 'lie' (story can mean a fabrication).
'involving' is an insertion indicator.
'donkey' becomes 'ass' (ass is a term for a donkey).
'lie' enclosing 'ass' is 'LASSIE'.
(Other definitions for lassie that I've seen before include "Film and TV dog" , "Screen canine" , "Collie featuring in many films" , "Young Scottish girl or Hollywood lost dog" , "TV/film dog" .)