Dig out an obscure inn for eating (6)
I believe the answer is:
dining
'for eating' is the definition.
(dining is a kind of eating)
'dig out an obscure inn' is the wordplay.
'out' indicates putting letters inside.
'an obscure' indicates an anagram.
'inn' anagrammed gives 'nin'.
'dig' enclosing 'nin' is 'DINING'.
(Other definitions for dining that I've seen before include "Making a meal of" , "Eating main meal" , "Supping" , "Eating the evening meal" , "at lunch?" .)