Ambassador boards cold ship for game (5)
I believe the answer is:
'for game' is the definition.
(chess is a kind of game)
'ambassador boards cold ship' is the wordplay.
'ambassador' becomes 'he' (His or Her Excellency).
'boards' means one lot of letters goes inside another.
'cold' becomes 'c' (eg on taps).
'ship' becomes 'SS' (prefix in ship names eg SS Great Britain).
'he' going into 'css' is 'CHESS'.
(Other definitions for chess that I've seen before include "Sixteen-men-a-side game" , "Ancient war game whose name may have derived for the Persian for 'king'" , "Pieces moved in this" , "Musical - board game" , "Board game of 13, 16 and 21" .)