Wordpress add short description on the custom post type page: The filter views_{$this->screen->id} is fired just after the title of post edit screen has been print to screen, so it's a safe place to just echo what you want. So you can simply do:

function.php

<?php

function post_type_desc( $views ){

    $screen = get_current_screen();
    $post_type = get_post_type_object($screen->post_type);

    if ($post_type->description) {
      printf('<h4>%s</h4>', esc_html($post_type->description)); // echo 
    }

    return $views; // return original input unchanged
}

add_filter("views_edit-POST_TYPE_HERE", 'post_type_desc');