The game for bigheaded fliers (5)
I believe the answer is:
bowls
'the game' is the definition.
(bowls is a kind of game)
'bigheaded fliers' is the wordplay.
'bigheaded' becomes 'b' (this might be a standard abbreviation I've not previously seen).
'fliers' becomes 'owls' (owl is a kind of bird).
'b'+'owls'='BOWLS'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for bowls that I've seen before include "Kitchen vessels" , "Throws or rolls a ball" , "Kitchen pots for storing" , "Game played on green" , "woods" .)