Tool used around the first game (5)
I believe the answer is:
lotto
'game' is the definition.
(the UK National Lottery)
'tool used around the first' is the wordplay.
'used' indicates anagramming the letters.
'around' indicates putting letters inside.
'the first' becomes 't' (1st letter of 'the').
'tool' with letters rearranged gives 'loto'.
'loto' enclosing 't' is 'LOTTO'.
(Other definitions for lotto that I've seen before include "Game of chance similar to bingo" , "National gambling game" , "Prize draw" , "chancy business" , "National game with large money prizes" .)