Servant with a bit of a black eye (6)
I believe the answer is:
lackey
'servant' is the definition.
(lackey is a kind of servant)
'a bit of a black eye' is the wordplay.
'a bit of' indicates the answer is hidden within the clue (I've seen 'a bit' mean this (the answer is formed by a bit of the clue)).
'LACKEY' is hidden within 'black eye'.
'with' acts as a link.
(Other definitions for lackey that I've seen before include "An archaic menial or follower" , "An old servant or slavish person" , "An archaic menial or servant" , "Liveried servant" , "Minion or servile follower" .)