Custom Post Removing 'add new'

I have the following custom page, not post..

This is from my functions.php.

function post_type_teaching() {

  register_post_type('teaching',
   array(
     'labels' => array(
     'name' => __( 'Teaching + Research' ),
     'singular_name' => __( 'Teaching + Research' ),
     //'add_new' => __( 'Add New' ),
     'add_new_item' => __( 'Add New Teaching + Research' ),
     'edit' => __( 'Edit' ),
     'edit_item' => __( 'Edit Teaching + Research' ),
     'new_item' => __( 'New Teaching + Research' ),
     'view' => __( 'View Teaching + Research' ),

     'view_item' => __( 'View Teaching + Research' ),
     'search_items' => __( 'Search Teaching + Research' ),
     'not_found' => __( 'No Teaching + Research found' ),
     'not_found_in_trash' => __( 'No Teaching + Research found in Trash' ),
     'parent' => __( 'Parent Teaching + Research' ),
     'capability_type' => 'page',
    ),
       'public' => true,
       'show_ui' => true,
       'menu_position' => 6,
    'exclude_from_search' => true,
    'hierarchical' => true,
    'supports' => array( 'title', 'editor', 'thumbnail' ),
    'query_var' => true
    )
    );

  }
   add_action('init', 'post_type_teaching');

The teaching page is one page that never needs to be removed or added to only edited.

So is there anyway i can remove, the ‘add new’ from the left column as well as the trash option within?

Cheers 🙂