Initially four of you entered residential hall (5)

I believe the answer is:

foyer

'hall' is the definition.
('foyer' can be a synonym of 'hall')

'initially four of you entered residential' is the wordplay.
'initially' indicates taking the first letters.
The first letters of 'four of you entered residential' is 'FOYER'.

(Other definitions for foyer that I've seen before include "Anteroom" , "Theatre public area" , "Reception room or waiting area" , "Reception lobby" , "Large entrance area" .)

I've seen this clue in The Telegraph.

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