In terms of larger projects, the Servo guys always seem to encourage people learning Rust to get involved. One of the projects I'm most interested in is Frank McSherry's timely/differental dataflow repos. I wanted a Rust implementation of Naiad when I first read the paper so I was quite pleased to see one of the authors do an implementation, even if it doesn't seem to be a full time pursuit.
[1] https://github.com/frankmcsherry/timely-dataflow/
Most first-rust-projects that are announced on reddit/discourse seem to be games (Piston), simple web apps, raytracers, or datastructures.
I agree that Clojure isn't suited to hard real time systems and it's not hard to come up with drawbacks to the above approach but you just happened to pick an example that a lot of people in the Clojure community seem to care about.
Well of course that's a technique but "another system" isn't Clojure. It does so happen that a Lisp language is especially fluent for programming audio processors because of its compiler-like expressions and macros.