How to add new item in menu_local?
In my case using hook_menu will never work. Then i have to use hook_menu_local_tasks_alter to make it work.
Here is how.

function manage_child_menu_local_tasks_alter(&amp;$data, $router_item, $root_path) {
   if ((arg(0) == 'node' || arg(0) == 'groups') &amp;&amp; arg(2) == '') {
   $nid = arg(1);
   $node = node_load($nid);
   if ($node-&gt;type == 'project_auction') {
     $link = menu_get_item("node/$nid/demo");
     $link['title'] = 'Auction List';
     $link['weight'] = 10;

     $data['tabs'][0]['output'][] = array(
       '#theme' =&gt; 'menu_local_task',
       '#link' =&gt; $link,
     );

     $data['tabs'][0]['count'] = $data['tabs']['0']['count'] + 1;
  }
 }
}