Acknowledge and allow to enter (5)
I believe the answer is:
admit
This clue is a double definition.
'acknowledge' is the first definition.
(synonyms)
'allow to enter' is the second definition.
(I've seen this in another clue)
'and' acts as a link.
(Other definitions for admit that I've seen before include "Recognise" , "permit to come in" , "Fess up" , "receive" , "Usher in" .)