Rust does not yet have local custom allocators ala C++. (You can change the global allocator, but this doesn't help the "memory arena" use case.) The feature is very much on the roadmap, though.
While this is true, this doesn't inherently mean you can't do this pattern. https://crates.io/crates/typed_arena for example. It depends on exactly how allocations and your data structure are tied together.
It would be amazingly handy if someday it was possible to direct Rust to make all heap allocations under a certain block within an arena. At the moment it looks like you have to rewrite any third party code that makes heap allocations to use the arena explicitly at each allocation.