Defeated player looks teary from time to time (5)
I believe the answer is:
loser
'defeated player' is the definition.
'looks teary from time to time' is the wordplay.
'from time to time' indicates alternate letters (letters removed on a regular basis).
'looks'+'teary'='looksteary'
The alternate letters of 'looksteary' are 'LOSER'.
(Other definitions for loser that I've seen before include "sad type?" , "Failed competitor" , "One who is always a failure" , "Non-achiever" , "One who frequently fails (colloq.)" .)