Chuck out former student after gym (5)
I believe the answer is:
expel
'chuck out' is the definition.
(synonyms)
'former student after gym' is the wordplay.
'former' becomes 'ex' (prefix meaning former or onetime).
'student' becomes 'l' (as in L-plates for learner drivers).
'after' is a charade indicator (letters next to each other).
'gym' becomes 'pe' (short for Physical Education).
'l' after 'pe' is 'pel'.
'ex'+'pel'='EXPEL'
(Other definitions for expel that I've seen before include "Force to leave" , "Eject (from school)" , "Drive out with force" , "Boot out" , "Possibly remove from club" .)