Have influence on game: it should give greater opening for current moves (5,6)
I believe the answer is:
swing bridge
'it should give greater opening for current moves' is the definition.
(a swing bridge makes room for boats on the current)
'have influence on game' is the wordplay.
'have influence on' becomes 'swing' (to swing a game is to affect the result unfairly).
'game' becomes 'bridge' (bridge is a kind of game).
'swing'+'bridge'='SWING-BRIDGE'
(Other definitions for swing bridge that I've seen before include "Movable crossing over stretch of water" , "Movable river/canal crossing" .)