The phrase "a sort of quiet" is correct and usable in written English.
It can be used to describe a type or quality of quietness that is not absolute but rather has a particular character or nuance.
Example: "There was a sort of quiet in the room that made everyone feel uneasy."
Alternatives: "a kind of silence" or "a type of stillness".
"I feel," Kerry said, "as much energy and a sort of quiet — that's a good word, a calm and confidence — about what I'm doing and how I'm approaching things as I ever have.
After the excerpt from "Ocean," Cunningham sat at a table in the middle of the room and talked, briefly and with a sort of quiet merriment, about the old dances and the new one.
By placing these vague references to language among the fallen trees and frozen highlights, Mr. Torlen adds a sort of quiet wisdom, as if the forest is trying to convey an inner calm born of the promise of the cycle of life.
"We're going to mock up something for my boys, so they've got a sort of quiet, cold version of the same thing that they can leap around with".
But this last year was marked by a sort of quiet final surrender by the film cadre: Arri, Panavision, and Aaton have all ceased production of film cameras.
"They have a sort of quiet dignity.
When I watched this scene for the very first time, I found myself occupying a sort of still, quiet concentration, like when you overhear people talking about you in another room and you have to lean in closer to get a better listen.
But they are shut tight for this one, giving the box a sort of eerie quiet.
I think that just a distance, a sort of a quiet observation of how that mechanism works, and how you could imagine they're feeling at a certain time is..
For a day and a half, I had been rehearsing these phrases with the proper expression on my face: a subdued, sort of quiet surprise.
The common reader – that phantasm dreamt up by writers, a sort of idealized perfect lover and quiet listener – is longer so perfect or so quiet.
