Warn area about British in part of Canada (7)
I believe the answer is:
alberta
'part of canada' is the definition.
('Alberta' is part of 'canada')
'warn area about british' is the wordplay.
'warn' becomes 'alert' (alerting is a kind of warning).
'area' becomes 'a' (maths abbreviation).
'about' means one lot of letters goes inside another.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'alert'+'a'='alerta'
'alerta' enclosing 'b' is 'ALBERTA'.
'in' acts as a link.
(Other definitions for alberta that I've seen before include "Bale rat out of Canada" , "Canadian province, capital Edmonton" , "Einstein" , "part of Canada" , "Banff province" .)