Story encapsulated by additional French playwright (7)
I believe the answer is:
moliere
'french playwright' is the definition.
(I've seen this before)
'story encapsulated by additional' is the wordplay.
'story' becomes 'lie' (I've seen this before).
'encapsulated by' is an insertion indicator (I've seen this in other clues).
'additional' becomes 'more' ('more' can be a synonym of 'additional').
'lie' put inside 'more' is 'MOLIERE'.
(Other definitions for moliere that I've seen before include "French dramatist" , "French playwright (Tartuffe)" , "C17 French playwright (Le Misanthrope)" , "17th century French playwright" , "Fr. comic dramatist" .)