Princess ain't crazy about admirer (7)
I believe the answer is:
infanta
'princess' is the definition.
(thesaurus)
'ain't crazy about admirer' is the wordplay.
'crazy' is an anagram indicator.
'about' means one lot of letters goes inside another.
'admirer' becomes 'fan' (fan is a kind of admirer).
'aint' anagrammed gives 'inta'.
'inta' enclosing 'fan' is 'INFANTA'.
(Other definitions for infanta that I've seen before include "Daughter of a Spanish or Portuguese king" , "member of the Spanish royal family" , "King of Spain's daughter" , "Royal personage" , "girl in foreign court" .)