Game everyone supports to avoid British (9)

'game' is the definition.
(ball game)

'everyone supports to avoid british' is the wordplay.
I cannot really understand how this works, but
'everyone' could be 'all' (all people) and 'all' is present in the answer.
'avoid' could be 'dodge' (dodging is a kind of avoiding) and 'dodge' is present in the answer.
'british' could be 'b' (abbreviation e.g. in 'BBC') and 'b' is found in the answer.
This accounts for all the letters.
This explanation may well be incorrect...