Old game medic slices Danish bread (5)
I believe the answer is:
ombre
'old game' is the definition.
(historical card game)
'medic slices danish bread' is the wordplay.
'medic' becomes 'MB' (Bachelor of Medicine).
'slices' is an insertion indicator (inserted letters slice their way in).
'danish bread' becomes 'ore' (Danish currency unit - 'bread' can mean money).
'mb' placed into 'ore' is 'OMBRE'.
(Other definitions for ombre that I've seen before include "With blending colours" , "Card game for three" , "Shaded" , "Card-game for three; rob me (anag.)" , "Three-player card game" .)