Jack moves first in this game (5)
I believe the answer is:
bowls
'this game' is the definition.
(bowls is a kind of game)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for bowls that I've seen before include "Throws or rolls a ball" , "Kitchen pots for storing" , "Kitchen vessels" , "woods" , "Rolls smoothly along the ground" .)