I'm currently building an application using gtk-rs using GTK4. To react to key presses the EventControllerKey can be used. This is added as a controller to the main window.

let control_key = gtk::EventControllerKey::new();

control_key.connect_key_pressed(move |_, key, _, _| {
    match key {
        gdk::Key::Right => { ... },
        gdk::Key::Left => { ... },
        gdk::Key::Up => { ... },
        gdk::Key::Down => { ... },
        _ => (),
    }
    glib::Propagation::Proceed
});
window.add_controller(control_key);