Old American seen around North Arkansas food store (7)
I believe the answer is:
granary
'food store' is the definition.
'granary' can be an answer for 'store' (granary is a kind of store). I'm unsure of the 'food' bit.
'old american seen around north arkansas' is the wordplay.
'old american' becomes 'gray' (I can't explain this - if you can you should believe this answer much more).
'seen around' indicates putting letters inside.
'north' becomes 'N' (abbreviation).
'arkansas' becomes 'ar' (abbreviation for the US state).
'n'+'ar'='nar'
'gray' placed around 'nar' is 'GRANARY'.
Can you help me to learn more?
(Other definitions for granary that I've seen before include "Harvest store" , "Grain storehouse" , "Storehouse for corn, etc" , "breadbasket" , "Store for, eg, corn" .)