Figure twelve featuring badger (7)
I believe the answer is:
nonagon
'figure' is the definition.
(type of geometrical figure)
'twelve featuring badger' is the wordplay.
'twelve' becomes 'noon' (twelve noon).
'featuring' is an insertion indicator.
'badger' becomes 'nag' (both can mean to annoy or complain at).
'noon' enclosing 'nag' is 'NONAGON'.
(Other definitions for nonagon that I've seen before include "Nine-sided figure" , "Figure with nine, twenty-one Dn" , "Nine sided figure" , "Nine-sided shape" , "Nine-sided polygon" .)