In showthread template find and remove:
<!-- Thread nav and post images -->
<table width="100%" border="0" cellpadding="0" cellspacing="0">
<tr>
<td width="100%"><smallfont color="{tableheadtextcolor}" class="thtcolor"><b>Thread</b></smallfont></td>
<td><a href="newthread.php?s=$session[sessionhash]&action=newthread&forumid=$forum[forumid]"><img src="{newthreadimage}" border="0" alt="Post New Thread"></a></td>
<td><normalfont> </normalfont></td>
<td><a href="newreply.php?s=$session[sessionhash]&action=newreply&threadid=$threadid"><img src="$replyclose" border="0" alt="Post A Reply"></a></td>
</tr>
</table>
<!-- /Thread nav and post images -->