Add count for new registered user in Users tab

Yes, there is. You can use admin_menu hook to loop through menu items and add span with notification. There are two classes that WP uses for these notifications update-plugins and awaiting-mod. The second one looks more appropriate in this case, I guess…

Here’s some code:

function add_user_menu_notification() {
    global $menu;

    $user_count = count_users();  // get whatever count you need
    $user_count = $user_count['avail_roles']['administrator'];

    if ( $user_count ) {
        foreach ( $menu as $key => $value ) {
            if ( $menu[$key][2] == 'users.php' ) {
                $menu[$key][0] .= ' <span class="awaiting-mod">' . $user_count . '</span>';
                return;
            }
        }
    }
}
add_action( 'admin_menu', 'add_user_menu_notification' );