Aussie native infiltrating company, genteel English establishment? (3,4)
I believe the answer is:
tea room
'genteel english establishment?' is the definition.
'aussie native infiltrating company' is the wordplay.
'aussie native' becomes 'roo' (short for kangaroo).
'infiltrating' indicates putting letters inside.
'company' becomes 'team' (I've seen this before).
'roo' placed into 'team' is 'TEA-ROOM'.
(Other definitions for tea room that I've seen before include "Place in which a cuppa is served" , "Place for light refreshments" , "Where light refreshments are served" , "Small restaurant or cafe" .)