Throw out former pupil following exercise (5)
I believe the answer is:
expel
'throw out' is the definition.
('expel' can be a synonym of 'throw out')
'former pupil following exercise' is the wordplay.
'former' becomes 'ex'.
'pupil' becomes 'l'.
'following' says to put letters next to each other.
'exercise' becomes 'pe' (Physical Education).
'l' put after 'pe' is 'pel'.
'ex'+'pel'='EXPEL'
(Other definitions for expel that I've seen before include "Eject (from school)" , "Drive away" , "Reject" , "Get rid" , "Oust" .)