Subdivision of British farm (6)
I believe the answer is:
branch
'subdivision' is the definition.
(I know that subdivision can be written as branch)
'british farm' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in BBC).
'farm' becomes 'ranch' (ranch is a kind of farm).
'b'+'ranch'='BRANCH'
'of' acts as a link.
(Other definitions for branch that I've seen before include "Part of tree/river" , "Part of organisation or tree" , "Division of some larger organisation" , "Division of a stem" , "Lateral extension of river or railway" .)