Strive to retain British feeling (4)
I believe the answer is:
vibe
'feeling' is the definition.
(I've seen this before)
'strive to retain british' is the wordplay.
'strive' becomes 'vie' (I've seen this in another clue).
'to retain' indicates putting letters inside.
'british' becomes 'b' (abbreviation e.g. in BBC).
'vie' enclosing 'b' is 'VIBE'.
(Other definitions for vibe that I've seen before include "Aura (colloq.)" , "Atmosphere, aura" , "Aura given off by person/place" , "Aura experienced instinctively" , "Atmosphere, feeling" .)