Beauty queen is mad with sexist (13)
I believe the answer is:
exquisiteness
'beauty' is the definition.
(exquisiteness is a kind of beauty)
'queen is mad with sexist' is the wordplay.
'mad with' indicates anagramming the letters.
'queen'+'is'='queenis'
'queenis' anagrammed with 'sexist' makes 'EXQUISITENESS'.
(Other definitions for exquisiteness that I've seen before include "Extreme beauty and delicacy" , "Beauty of well-made object" .)