Old writer briefly covers a game (5)
I believe the answer is:
quail
'game' is the definition.
(I've seen this before)
'old writer briefly covers a' is the wordplay.
'old writer' becomes 'quill' (I've seen this before).
'briefly' means to remove the last letter.
'covers' means one lot of letters goes inside another.
'quill' with its last letter taken away is 'quil'.
'quil' enclosing 'a' is 'QUAIL'.
(Other definitions for quail that I've seen before include "Shrink; a bird" , "Game bird - cower" , "Cower before the game-bird?" , "Small bird of the partridge family" , "Game bird; flinch" .)