Fearless British getting on (4)
I believe the answer is:
bold
'fearless' is the definition.
('bold' is associated in meaning with 'fearless')
'british getting on' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'getting on' becomes 'old' ('getting on a bit' means 'old').
'b'+'old'='BOLD'
(Other definitions for bold that I've seen before include "Conspicuous" , "like Ben Battle" , "Valiant" , "Brash" , "Intrepid" .)