Un-promote all other nodes when one node is promoted to front page
In the views, you can simply sort the view by updated date on filtered promoted nodes. I think this will solve the issue without any custom code. This might not work in all cases. It will fail when content writer promotes a new node, then updates old promoted node.

You can use below code. For your specific case, you can use $base_root to apply the change on a particular site only.

function MY_MODULE_node_presave($node){
  // if $base_root is equal to my.specific.domain.site, then perform the db_update.
  if ($node-&gt;type == 'career' &amp;&amp; $node-&gt;promote == 1) {   
    $update = db_update('node')
      -&gt;fields(array('promote' =&gt; 0))
      -&gt;condition('node.promote', 1, '=')
      -&gt;condition('node.type', 'career', '=')
      -&gt;condition('node.nid', $node-&gt;nid, '&lt;&gt;');
    $update.execute();
    // Do this if you still face the problem. Also please comment if node_revision update was necessary.
    // $update = db_update('node_revision')
    //   -&gt;fields(array('promote' =&gt; 0))
    //   -&gt;condition('node.promote', 1, '=')
    //   -&gt;condition('node.type', 'career', '=')
    //   -&gt;condition('node.nid', $node-&gt;nid, '&lt;&gt;');
    // $update.execute();     
  }
}