Author to a greater degree pens story (7)
I believe the answer is:
moliere
'author' is the definition.
(Moliere is an example)
'to a greater degree pens story' is the wordplay.
'to a greater degree' becomes 'more' (I've seen this in another clue).
'pens' means one lot of letters goes inside another (inserted letters are held or penned in).
'story' becomes 'lie' (story can mean a fabrication).
'more' placed around 'lie' is 'MOLIERE'.
(Other definitions for moliere that I've seen before include "Fr. comic dramatist" , "Fr. dramatist (Tartuffe)" , "French writer" , "C17 French playwright (Le Misanthrope)" , "French dramatist" .)