Bloke’s participating in Civil Service game (5)
I believe the answer is:
chess
'game' is the definition.
(board game)
'bloke's participating in civil service' is the wordplay.
'bloke's' becomes 'he's' ('he' refers to a man).
'participating in' is an insertion indicator.
'civil service' becomes 'CS' (abbreviation).
'hes' going into 'cs' is 'CHESS'.
(Other definitions for chess that I've seen before include "Musical - board game" , "A game of skill" , "Board game for two players" , "Pure-skill board game" , "Ancient war game whose name may have derived for the Persian for 'king'" .)