$('.delete_btn').click(function(){
var key = $(this).attr("key");
$('.client'+key).remove();
});
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<table id="client_table">
<tbody>
<tr class="client1">
<td>1</td>
<td>Content</td>
<td><input class="delete_btn" type="button" key="1" value="Delete"></td>
</tr>
</tbody>
</table>