Division of British farm (6)
I believe the answer is:
branch
'division' is the definition.
(branch is a kind of division)
'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 "regional office" , "Offshoot or subdivision" , "Division of a stem" , "Tree limb" , "One shop of a chain" .)