Show a different navigation menu to logged-in users in WordPress. Source: http://www.wpbeginner.com/wp-themes/how-to-show-different-menus-to-logged-in-users-in-wordpress/

show-different-menu.php

<?php

//* Show a different navigation menu to logged-in users in WordPress
function prefix_show_different_menu($args = '') {
    if (is_user_logged_in()) {
        $args['menu'] = 'logged-in'; // Navigation menu's name when users are logged-in
    } 
    else {
        $args['menu'] = 'logged-out'; // Navigation menu's name when users are not logged-in
    }
    return $args;
}
add_filter('wp_nav_menu_args', 'prefix_show_different_menu');