Appear depressed, but work through debilitating condition (4)
I believe the answer is:
mope
'appear depressed' is the definition.
(to mope is act depressed)
'work through debilitating condition' is the wordplay.
'work' becomes 'op' (common abbreviation for 'opus').
'through' indicates putting letters inside (inserted letters go through the word).
'debilitating condition' becomes 'ME' (myalgic encephalomyelitis).
'op' put into 'me' is 'MOPE'.
'but' is the link.
(Other definitions for mope that I've seen before include "Feel dejected and listless" , "Pine - sulk" , "Be listless or depressed" , "Yield to low spirits with an odd poem" , "Be mildly depressed" .)