Game to do with passing round dictionary before finishing early (3,4)
I believe the answer is:
roe deer
'game' is the definition.
'to do with passing round dictionary before finishing early' is the wordplay.
'to do with' becomes 're' (regarding).
'passing round' indicates putting letters inside.
'dictionary' becomes 'oed' (Oxford English Dictionary).
'before' becomes 'ere' (usually literary).
'finishing early' means to remove the last letter.
're' placed around 'oed' is 'roede'.
'ere' with its final letter taken off is 'er'.
'roede'+'er'='ROE-DEER'
(Other definitions for roe deer that I've seen before include "Some wildlife" , "Small cervid mammal" , "Native wild animal" , "beast" , "Cervine animal" .)