Author of additional gripping story (7)
I believe the answer is:
moliere
'author' is the definition.
(Moliere is an example)
'additional gripping story' is the wordplay.
'additional' becomes 'more' (synonyms).
'gripping' indicates putting letters inside (inserted letters are gripped).
'story' becomes 'lie' (story can mean a fabrication).
'more' placed around 'lie' is 'MOLIERE'.
'of' is the link.
(Other definitions for moliere that I've seen before include "French playwright (Tartuffe)" , "C17 French playwright (Le Misanthrope)" , "French dramatist" , "French writer" , "Fr. dramatist (Tartuffe)" .)