How can I NOT show the Request new password tab within the /user (login) page for one particular user
If you just wish to hide the tab, you can do that by using the Tab Tamer module. However, the user would still be able to access the form through the URL http://&lt;yoursite&gt;/user/password.

If you wish to disable (along with hiding) the password tab, you can implement the hook_menu_alter().

function MODULE_menu_alter(&amp;$items) {
  //condition to check the user
  global $user;
  if($user-&gt;id == '&lt;USER_ID_OF_THE_USER&gt;') { //can use $user-&gt;name as well
    $items['user/password']['access callback'] = FALSE;
  }
}