Fat friend, briefly ill, after doctor (4,3)
I believe the answer is:
palm oil
'fat' is the definition.
(I know that palm oil is a type of vegetable oil)
'friend briefly ill after doctor' is the wordplay.
'friend' becomes 'pal' (pal can mean a friend).
'briefly' means to remove the last letter.
'after' is a charade indicator (letters next to each other).
'doctor' becomes 'mo' (medical officer).
'ill' with its last letter taken away is 'il'.
'il' after 'mo' is 'moil'.
'pal'+'moil'='PALM-OIL'
(Other definitions for palm oil that I've seen before include "Product of tropical tree" , "Vegetable fat" , "Fatty tree product" .)