Bird kept in by unpopular headmaster (4)
I believe the answer is:
rhea
'bird' is the definition.
(I know that rhea is a type of flightless bird)
'in by unpopular headmaster' is the wordplay.
'in' says the answer is hidden in the clue.
'RHEA' is hidden in the letters of 'by unpopular headmaster'.
'kept' acts as a link.
(Other definitions for rhea that I've seen before include "Fast runner" , "New World ostrich" , "South American bird resembling the ostrich" , "S American runner" , "Flightless bird -- satellite of Saturn" .)