Her master has a bewildered air (5)
I believe the answer is:
maria
'her' is the definition.
(I've seen this before)
'master has a bewildered air' is the wordplay.
'master' becomes 'ma' (Master of Arts).
'has' is an insertion indicator.
'a bewildered' indicates anagramming the letters.
'air' with letters rearranged gives 'ari'.
'ma' enclosing 'ari' is 'MARIA'.
(Other definitions for maria that I've seen before include "Dark planes on the moon; girl's name" , "Von Trapp star" , "Lady" , "Heroine of West Side Story" , "Lunar plains; girl's name" .)