Create vector of trait objects

There are several issues with your code. The first is that you're creating a Vec<Box<Link>> instead of a Vec<Box<Speak>>. By default Box::new (foo) creates a box of the same type as foo. If you want a box of some trait implemented by foo, you need to be explicit:

links.push(Box::new(Link { attr: href }) as Box::<dyn Speak>);

Playground

However this gives two new errors:

error[E0716]: temporary value dropped while borrowed
 --> src/lib.rs:7:20
  |
7 |         let href = myfile.path().to_str().unwrap();
  |                    ^^^^^^^^^^^^^                  - temporary value is freed at the end of this statement
  |                    |
  |                    creates a temporary which is freed while still in use
8 |         links.push(Box::new(Link { attr: href }) as Box::<dyn Speak>);
  |                    ----------------------------- cast requires that borrow lasts for `'static`

error[E0596]: cannot borrow `links` as mutable, as it is not declared as mutable
 --> src/lib.rs:8:9
  |
4 |     let links = Vec::new();
  |         ----- help: consider changing this to be mutable: `mut links`
...
8 |         links.push(Box::new(Link { attr: href }) as Box::<dyn Speak>);
  |         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ cannot borrow as mutable

The first error is because your Link struct borrows a string from entry, but entry only lives as long as the current loop iteration. Even though the error states that the cast requires a 'static lifetime, you would get a similar error if you were simply trying to build a Vec<Link> without casting (playground). You need to change the definition of your Link struct to contain an owned string:

struct Link {
    attr: String,
}
impl Speak for Link {
    fn speak(&self) -> String {
        self.attr.clone()
    }
}

The second error is easier and can be fixed simply by following the compiler suggestion and replacing let links = … with let mut links = ….

Full working example:

use std::fs;

fn main() {
    let mut links = Vec::new();
    for entry in fs::read_dir("my_dir").unwrap() {
        let myfile = entry.unwrap();
        let href = myfile.path().to_str().unwrap().to_string();
        links.push(Box::new(Link { attr: href }) as Box::<dyn Speak>);
    }

    let link_objects = ListOfTraitObjects {
        trait_objects: links,
    };
    for link in link_objects.trait_objects.iter() {
        println!("{}", link.speak());
    }
}
trait Speak {
    fn speak(&self) -> String;
}

struct ListOfTraitObjects {
    trait_objects: Vec<Box<dyn Speak>>,
}

struct Link {
    attr: String,
}
impl Speak for Link {
    fn speak(&self) -> String {
        self.attr.clone()
    }
}

Playground

The same fixes can be applied to your iterator-based solution:

let links = fs::read_dir("my_dir").unwrap();
let links: Vec<_> = links
    .map(|file| {
        let myfile = file.unwrap();
        let href = myfile.path().to_str().unwrap().to_string();
        Box::new(Link { attr: href }) as Box<dyn Speak>
    })
    .collect();

Playground