make a move

1. To take a decisive action intended to achieve a goal or start the process of achieving it. Lisa really seems like she likes you, dude—now's the time to make a move! Greg told me that he intends to make a move to get the boss's attention at this meeting, so I'm curious to see what he has planned.

2. To begin leaving some place. We told the babysitter we'd be back by 10, so we should start making a move.

make a move

1 take action. 2 start on a journey; leave somewhere. British

make a ˈmove

1 (British English, informal) leave one place in order to go to another: It’s getting late. I think it’s time we made a move. ♢ I’ve been in this job far too long already, it’s time I made a move.
2 (also make your ˈmove) do the action that you intend to do or need to do in order to achieve something: We’re waiting to see what our competitors will do before we make a move. ♢ The rebels waited until nightfall before making their move.

This phrase refers to moving your pieces in a game such as chess.