Great line in cut story (5)
I believe the answer is:
fable
'story' is the definition.
(I know that fable is a type of story)
'great line in cut' is the wordplay.
'great' becomes 'fab' (short for fabulous).
'cut' suggests deleting specific letters.
'line' with 'in' removed is 'le'.
'fab'+'le'='FABLE'
(Other definitions for fable that I've seen before include "there may be a moral to it" , "Moral tale" , "Old wives' tale" , "Aesop story" , "Story, often with moral" .)