Put out of school, former student lurks outside gym (5)
I believe the answer is:
expel
'put out of school' is the definition.
'former student lurks outside gym' is the wordplay.
'former' becomes 'ex'.
'student' becomes 'l'.
'lurks outside' means one lot of letters goes inside another.
'gym' becomes 'pe'.
'ex'+'l'='exl'
'exl' going around 'pe' is 'EXPEL'.
(Other definitions for expel that I've seen before include "Boot out" , "Deport" , "Drive out - eject" , "Evict" , "Drive out with force" .)