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' indicates anagramming the letters.
'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" .)