From Kenya, run delicatessen somewhere in Sussex (7)
I believe the answer is:
arundel
'somewhere in sussex' is the definition.
(Sussex town)
'from kenya run delicatessen' is the wordplay.
'from' indicates a hidden word.
'ARUNDEL' is hidden in the letters of 'kenya run delicatessen'.
(Other definitions for arundel that I've seen before include "English public school" , "Castle in W. Sussex" , "somewhere in W Sussex" , "Norfolk seat" , "West Sussex town with a castle" .)