She worked in the civil service game (5)
I believe the answer is:
chess
'game' is the definition.
(chess game is a kind of game)
'she worked in the civil service' is the wordplay.
'worked' is an anagram indicator.
'in the' means one lot of letters goes inside another.
'civil service' becomes 'cs'.
'she' with letters rearranged gives 'hes'.
'hes' going inside 'cs' is 'CHESS'.
(Other definitions for chess that I've seen before include "Ancient war game whose name may have derived for the Persian for 'king'" , "A game of skill" , "Game with kings and queens" , "Game involving mates" , "that has over thirty men on board" .)