Female pupil ultimately out of favour (4)
I believe the answer is:
bess
'female' is the definition.
(woman's name)
I can't explain the remainder of the clue.
(Other definitions for bess that I've seen before include "Our Good Queen" , "Elizabeth (dim.)" , "Operatic mate for Porgy" , "Nickname for English queen" , "Black - was Dick Turpin's horse" .)