Hairdresser’s establishment (5)
I believe the answer is:
salon
'hairdresser's establishment' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for salon that I've seen before include "Drawing-room" , "Elegant room - for hairdresser?" , "Beauty parlour" , "Reception room in grand house" , "Parisian art exhibition" .)