Possibly settles on giving up southern food (4)
I believe the answer is:
eats
'food' is the definition.
(eats is a kind of food)
'possibly settles on giving up southern' is the wordplay.
'possibly settles' becomes 'seats' (to seat someone at a table is to settle them).
'on giving up' is a deletion indicator.
'southern' becomes 's' (abbreviation).
'seats' with 's' taken out is 'EATS'.
(Other definitions for eats that I've seen before include "Munches" , "Scoffs" , "Takes food" , "Comestibles" , "Provisions" .)