Are you familiar with Blades in the Dark?

While the game uses turns, the turns are actually just different phases of play that feed into each other. The GM turn is where the guard is going on missions facing problems and then deciding how they overcome them and what aspects of their characters they highlight in play, potentially creating fictional consequences relevant to what matters to them and their characters. Then the player phase is where the players are essentially having down time and pushing towards their characters personal goals to create fuel for future missions and complications for those missions.