Offshoot of British farm (6)
I believe the answer is:
branch
'offshoot' is the definition.
(synonyms)
'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' is the link.
(Other definitions for branch that I've seen before include "Bough - offshoot - secondary office" , "Offshoot or subdivision" , "Secondary stem" , "Division of some larger organisation" , "division within large organisation" .)