Rude gesture given with little hesitation in game (7)
I believe the answer is:
snooker
'game' is the definition.
(snooker is a game)
'rude gesture given with little hesitation' is the wordplay.
'rude gesture' becomes 'snook' (I've seen this in another clue).
'given with' is a charade indicator (letters next to each other).
'little hesitation' becomes 'er' (expression used when hesitating).
'snook'+'er'='SNOOKER'
'in' acts as a link.
(Other definitions for snooker that I've seen before include "check?" , "Indoor ball game" , "put in an awkward position" , "Cue sport" , "Ballgame" .)