If you want to get something that you could just buy, just buy it.
You can also get new gear when you take certain improvements.
If you want something that you just couldn’t buy (like a flamethrower, or a magical artifact), or something you don’t have the resources to get, then you need to do something special (like call in a favor, or steal it). Tell the Keeper what you’re doing, and play through the acquisition attempt to see how well it works.
The same thing can apply if you want an ally, a team under your command, or something else hard to arrange (like an Expert’s haven).
If you do everything necessary to get the new gear, well, then you get it (even without using an improvement or anything like that).