Deploy the hand Q

 Political Action

Requires a ready archbishop, cardinal or regent.
Choose one or more Methuselahs who do not have a target counter. Successful referendum means each chosen Methuselah gets a target counter. During his or her untap phase, a Methuselah with a target counter chooses one of his or her ready minions, who takes 2 unpreventable damage. A Methuselah may burn the Edge to burn his or her target counter.

If I have been given a target counter, but I get the edge, shall I wait till my next untap phase to burn it (in order to burn the counter) or I can do it any time?