British to grant vote (6)
I believe the answer is:
ballot
'vote' is the definition.
(balloting is a kind of voting)
'british to grant' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'to grant' becomes 'allot' (synonyms).
'b'+'allot'='BALLOT'
(Other definitions for ballot that I've seen before include "System of voting secretly" , "Vote or suffrage" , "Plebiscite" , "Voting paper" , "Single or collective vote" .)