I think in literary fiction you're a little less likely to be pulled along by the need to know what happens next. Often you're more engaged with the voice of the protagonist than with the plot. (I think it's rarer for teenagers to fall in love with beautiful words - but it does happen!) So I think the suspense can be turned down a little bit. But not all the way down. Especially for YA, there is a lot of great YA literary fiction that is not at all "quiet."
I think foreshadowing can be effective at building suspense. Whether it's by direct statement or a more subtle sense of foreboding, I think little clues about what's coming up can add into the suspense.
If I could overgeneralize about the difference between more commercial/plotty fiction and more literary fiction, I think literary fiction is more likely to get deeply into a character's heart and mind, and, for example, the small actions that wound and heal a friendship - you care because you know the character, and you see yourself or people you care about in the character's actions. In more commercial fiction, the issues are ones we can relate to right away even when they're more broadly sketched out.
But I think in writing literary fiction that's readable and suspenseful, it's important to remember that thoughts and emotions come out in actions, not just in internal monologues. And it's a delicate balance to create scenes that aren't melodramatic but also aren't just interiorized.
When you read Ellen Klages's "The Green Glass Sea," she depicts so clearly how the friendship between Dewey and Suze goes on in fits and starts, breaking and reforming, and it's not melodramatic - you want to keep reading because it feels so real. Reading "Looking For Alaska," that's EXACTLY how it feels to care deeply about someone teetering on the brink of self-destruction. And what a really great litfic YA novel does is relate to the reader's feelings, validate those feelings, and ultimately bring some catharsis to those feelings. The character may not be able to triump over his problem, but he can find meaning in it, he can grow as a person, he can emerge with the strength to face his future - and again, this can't be completely interior; it has to be expressed in plot, even if the plot is quiet and subtle.