Extraordinarily persistent beauty (10)
I believe the answer is:
prettiness
'beauty' is the definition.
(I know that prettiness is a type of beauty)
'extraordinarily persistent' is the wordplay.
'extraordinarily' is an anagram indicator (I've seen this in other clues).
'persistent' is an anagram of 'PRETTINESS'.
(Other definitions for prettiness that I've seen before include "1 across (anag)" , "Attractive quality" , "13 [ATTRACTIVE] state" .)