Bizarrely persistent charm (10)
I believe the answer is:
prettiness
'charm' is the definition.
(thesaurus)
'bizarrely persistent' is the wordplay.
'bizarrely' indicates anagramming the letters.
'persistent' anagrammed gives 'PRETTINESS'.
(Other definitions for prettiness that I've seen before include "1 across (anag)" , "Attractive quality" , "13 [ATTRACTIVE] state" .)