Give graduate students this game (8)
I believe the answer is:
handball
'this game' is the definition.
(I've seen this before)
'give graduate students' is the wordplay.
'give' becomes 'hand' ('hand' can be a synonym of 'give'**).
'graduate' becomes 'ba'.
'students' becomes 'll'.
'hand'+'ba'+'ll'='HANDBALL'
(Other definitions for handball that I've seen before include "Game played in a walled court" , "kind of foul" , "Offence from soccer" .)