Author of extra gripping story (7)
I believe the answer is:
moliere
'author' is the definition.
(Moliere is an example)
'extra gripping story' is the wordplay.
'extra' becomes 'more' (both can mean additional).
'gripping' indicates putting letters inside (inserted letters are gripped).
'story' becomes 'lie' (story can mean a fabrication).
'more' placed around 'lie' is 'MOLIERE'.
'of' acts as a link.
(Other definitions for moliere that I've seen before include "French writer" , "Fr. dramatist (Tartuffe)" , "Fr. comic dramatist" , "17th century French playwright" , "French dramatist" .)