Outsider is dying, feverish (4,4)
I believe the answer is:
long shot
'outsider' is the definition.
(I've seen this before)
'is dying feverish' is the wordplay.
'is dying' becomes 'longs' (to be dying for something is to long for it).
'feverish' becomes 'hot'.
'longs'+'hot'='LONG SHOT'
(Other definitions for long shot that I've seen before include "Very chancy venture" , "A wild venture or guess - even for marksman?" , "Something with slight chance of success" , "An attempt unlikely to be successful" , "What paparazzi might get" .)