The full complement of men on board? (5,3)
I believe the answer is:
chess set
'the full complement of men on board?' is the definition.
(men can mean chess pieces)
'of men on board?' is the wordplay.
'of men' becomes 'set' (I can't justify this - if you can you should believe this answer much more).
'on' is a charade indicator (letters next to each other).
'board?' becomes 'chess' (chess board is a kind of board).
'set' after 'chess' is 'CHESS SET'.
Can you help me to learn more?
(Other definitions for chess set that I've seen before include "It's played on a chequered board with 32 pieces" , "King, pawns etc." , "Game with kings, queens and bishops" , "It's played with kings, queens and bishops" , "men, along with the board" .)