We know how things work in a dungeon: go in turns; when the players do certain things (like go in rooms), certain things happen (like they see what's in the room, have an encounter); and as the turns proceed, there's a time-pressure chance of badness: wandering monster checks.
This works really well. It's easy and clear.
So let's pull it back and toss it over the whole game.
I'm running a thieves guild game. When not in a dungeon or whatever, the game goes in turns. I ask Player 1, what do you do? We resolve it: maybe he wanted to go shop for some gear. Then I ask Player 2 what he wants to do. Etc. Eventually, on say Player 4's turn, they agree to head for the dungeon.
Here's the thing: at the start of each turn, I'm rolling the macro equivalent of wandering monsters checks. (It's a 1 on a d10 at start of each turn.)
What's the translation? In a dungeon, the time pressure threat is monsters.
In the macro game, you'll need to customize it to your campaign.
In my campaign, the always-on threat is war between the thieves guilds and pressure from the law. Specific characters have their own threats too. Others might pop up.
I call these "looming crises" instead of wandering monsters, but they work exactly the same way and are just as easy to work.
You can have multiple checks if you want: a general one, a specific one to represent the hot war going on with the River Rats, another one to represent the ongoing murder investigation against one of the PCs, another to represent the spread of the abyssal plague, etc.
And optionally step up/down the check die as things get hotter/colder.
Make yourself some tables, roll on them, and interrupt with the badness.