He's after unfinished fast food (6)
I believe the answer is:
quiche
'food' is the definition.
(quiche is a kind of food)
'he's after unfinished fast' is the wordplay.
'he' becomes 'Che'.
'after' means one lot of letters go next to another.
'unfinished fast' becomes 'qui' (I am not sure about this - if you are sure you should believe this answer much more).
'che' after 'qui' is 'QUICHE'.
Can you help me to learn more?
(Other definitions for quiche that I've seen before include "Savoury egg-based flan" , "Baked egg flan" , "Egg dish" , "Tart filled with savoury ingredients" , "Savoury tart with egg-based filling" .)