There is no need to put " " around a variable name, you can just set it directly. So in your case, the code should be even a little simpler like this:
<?php
$date = $row_renew_list['date'];
$newdate = strtotime ( '+1 year' , strtotime ( $date ) ) ;
$newdate = date ( 'Y-m-d' , $newdate );
echo $newdate;
?>
</span></span>
-justin