Update the form action from:
action="linked_clients.php"
to:
action="linked_clients.php?AccountantID=<?php echo(intval($_GET['AccountantID'])); ?>"
Your page depends on the AccountantID in the url to show the correct result and it isn't getting passed in the form action.
Another thing, is that I couldn't even type into the form field for the search in Firefox. I had to add: style="clear:both" to the div:
<div class="col-lg-12">
You will want to fix that before going live.