Moon, or half moon, seen above gym (4)
I believe the answer is:
mope
'moon' is the definition.
(I've seen this before)
'half moon seen above gym' is the wordplay.
'half' indicates taking half.
'seen above' is a charade indicator (letters next to each other) (in a down clue, some letters go above others).
'gym' becomes 'pe' (Physical Education).
'moon' halved is 'mo'.
'mo'+'pe'='MOPE'
'or' is the link.
(Other definitions for mope that I've seen before include "Languish" , "Misery guts" , "Brood over a poem" , "Pine - sulk" , "Go gloomily about" .)