Secondary navigation menu on one page

If you need this menu on one page only, let’s say About Us (slug: about-us), you can easily add a conditional like this in pages.php at the place where you want the menu to appear:

if (is_page('about-us')) {
  wp_nav_menu( 
    array( 
        'theme_location' => 'secondary-menu', 
        'menu_class'     => 'secondary', 'fallback_cb' => ''
        )); 
  }

Remember that if you have a third party theme, you should build a child theme for this page, because else your adaptation will be lost when the theme is updated.