Quiet game ultimately inviting dismissive gesture (5)
I believe the answer is:
shrug
'dismissive gesture' is the definition.
(I've seen this in another clue)
'quiet game ultimately inviting' is the wordplay.
'quiet' becomes 'sh' ('sh' is used to tell someone to be quiet).
'game' becomes 'RU' (rugby union).
'ultimately' indicates one should take the final letters.
The last letter of 'inviting' is 'g'.
'sh'+'ru'+'g'='SHRUG'
(Other definitions for shrug that I've seen before include "Expression of unconcern" , "display nonchalance" , "So-what gesture" , "Brush off" , "Expression of indifference" .)