Greedily devours food, extremely tasty, in mess (6)
I believe the answer is:
pigsty
'mess' is the definition.
(pigsty can mean somewhere dirty or messy)
'greedily devours food extremely tasty' is the wordplay.
'greedily devours food' becomes 'pigs' (as in pigging out on food).
'extremely' means to remove the middle letters (only the extremes of the word are used).
'tasty' with its centre removed is 'ty'.
'pigs'+'ty'='PIGSTY'
'in' is the link.
(Other definitions for pigsty that I've seen before include "Porker pen" , "dump" , "Dirty domicile" , "Without boots" , "Dirty place; animal pen" .)