In Burning Wheel (both Gold and Revised; these rules are nearly identical), the Circles attribute represents people you might already know, or at least have some connection with through mutual contacts. You can make a roll to find someone in your extended social network has something you need, whether that's a set of tools you can borrow to fix your boat or a critical clue that will resolve an entire story arc. It's a pretty awesome ability.
What Circles doesn't let you do is just make people pop up everywhere. Like, if my character has just crossed the ocean to visit a new city, my ability to use Circles will be extremely limited.
However, let's say that, in that situation, I still need something that would normally be under the purview of Circles — information, illicit goods, a friendly-ish face I could persuade to take me in for a few days, &c. Normally this is all stuff you'd get with Circles and some extra minor effort, like a social skill test. When Circles isn't appropriate, what should I be doing, narratively and mechanically, to achieve similar results?