I don't think there is. It would be nice if we could force the pop-up to appear when clicking on the star icon.
I've only found two ways to expend prestige. The first is the daily pop-up with five options (naturalist, aerial survey, etc.), and the second is an option when lower-class workers arrive. If you've got 3+ prestige, you can spend it then to find at least one more laborer, and maybe more. Events can affect your prestige, and you could perhaps say that taking in stolen goods is a way to 'spend' prestige for them later, but that's even more unreliable. You're right that it would be helpful to have a list of prestige expenditures available, though that would have to be balanced against the ability to buy multiple sets of soldiers and overseers on-demand. What's needed—and I personally don't think this is a high priority compared to everything else, though I may be in the minority here—is variety. I'm fine with prestige being spent only when the game prompts you to spend it. I do think new and interesting ways of doing so are needed soon-ish. (Wouldn't it be fun to hire Inquisitors to root out cults and other anti-Imperial sentiment? Or a delivery of random non-food items from a friend "back home"? Or hiring entertainers to briefly assuage your colonists' frustrations?) Still, you're right that prestige sort of feels like a useless 'score' mechanic once you hit the mid- to late-game.
