Writer added gripping story (7)
I believe the answer is:
moliere
'writer' is the definition.
(Moliere is an example)
'added gripping story' is the wordplay.
'added' becomes 'more' (similar in meaning).
'gripping' is an insertion indicator (inserted letters are gripped).
'story' becomes 'lie' (story can mean a fabrication).
'more' going around 'lie' is 'MOLIERE'.
(Other definitions for moliere that I've seen before include "Fr. dramatist (Tartuffe)" , "French dramatist" , "C17 French playwright (Le Misanthrope)" , "French writer" , "Fr. comic dramatist" .)