Stick around, mind in a whirl, for the game (9)
I believe the answer is:
badminton
'game' is the definition.
(badminton is a kind of game)
'stick around mind in a whirl' is the wordplay.
'stick' becomes 'baton' (term for a stick or staff).
'around' indicates putting letters inside.
'in a whirl' indicates anagramming the letters.
'mind' is an anagram of 'dmin'.
'baton' going around 'dmin' is 'BADMINTON'.
'for the' acts as a link.
(Other definitions for badminton that I've seen before include "in which rackets are involved" , "Seat of the Duke of Beaufort - racket game" , "court action" , "Game with shuttlecocks" , "Racquet sport" .)