Above river, study game (7)
I believe the answer is:
contest
'game' is the definition.
(thesaurus)
'above river study' is the wordplay.
'above' is a charade indicator (letters next to each other) (in a down clue, some letters go above others).
'river' becomes 'test' (the River Test).
'study' becomes 'con' (con can informally mean to study).
'test' after 'con' is 'CONTEST'.
(Other definitions for contest that I've seen before include "Tournament" , "Oppose - competition" , "Competition or conflict" , "Match" , "Competition; dispute" .)