Fat fellow fronting political party (4)
I believe the answer is:
flab
'fat' is the definition.
(flab is a kind of fat)
'fellow fronting political party' is the wordplay.
'fronting' suggests taking the first letters (I've seen 'front' mean this).
'political party' becomes 'lab'.
The initial letter of 'fellow' is 'f'.
'f'+'lab'='FLAB'
(Other definitions for flab that I've seen before include "Fat acquired by over-eating" , "Loose body fat" , "Loose flesh; fat" , "Unwanted body fat" , "Soft loose flesh" .)