...that incorporates British river (5)
I believe the answer is:
yukon
'river' is the definition.
(I know that Yukon is a river)
'that incorporates british' is the wordplay.
'that' becomes 'yon' (archaic term meaning 'that').
'incorporates' is an insertion indicator.
'british' becomes 'uk' (Great Britain).
'yon' enclosing 'uk' is 'YUKON'.
(Other definitions for yukon that I've seen before include "Territory of NW Canada, east of Alaska" , "North American territory" , "remote territory" , "Canadian Gold Rush area" , "Territory of northwest Canada" .)