Exclusive pub with beer oddly missing (5)
I believe the answer is:
inner
'exclusive' is the definition.
(I've seen this before)
'pub with beer oddly missing' is the wordplay.
'pub' becomes 'inn' (an inn is a type of pub).
'with' is a charade indicator (letters next to each other).
'oddly missing' indicates alternate letters (letters in odd-numbered positions removed).
The alternate letters of 'beer' are 'er'.
'inn'+'er'='INNER'
(Other definitions for inner that I've seen before include "Situated within" , "Nearer to the centre, deeper" , "Target zone" , "Central area of a city, often old" , "Ring round bulls-eye" .)