Let everybody out, do we? (7)
I believe the answer is:
allowed
'let' is the definition.
(to allow something is to let it happen)
'everybody out do we?' is the wordplay.
'everybody' becomes 'all' (all people).
'out' is an anagram indicator.
'do'+'we'='dowe'
'dowe' anagrammed gives 'owed'.
'all'+'owed'='ALLOWED'
(Other definitions for allowed that I've seen before include "Given the chance" , "Acknowledged" , "Given permission" , "Permitted and granted" , "permissible" .)