Old exercise left to throw out (5)
I believe the answer is:
expel
'throw out' is the definition.
(I know that throw out can be written as expel)
'old exercise left' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'exercise' becomes 'pe' (Physical Education).
'left' becomes 'l' (common abbreviation).
'ex'+'pe'+'l'='EXPEL'
'to' acts as a link.
(Other definitions for expel that I've seen before include "Eject (from school)" , "Drive out - dispossess" , "Get rid" , "Evict" , "Kick out" .)