参考ソース例
<?php
$taxonomy_name = 'cat'; //※例)タクソノミー名
$term_id = 111; //※例)親ターム番号
$termchildren = get_term_children( $term_id, $taxonomy_name );
foreach ( $termchildren as $child ) :?>
<?php $term = get_term_by( 'id', $child, $taxonomy_name );?>
<li>
<a href="<?php echo get_term_link( $child, $taxonomy_name );?>">
<span><?php echo $term->name; //ターム名 ?></span>
</a>
</li>
<?php endforeach; ?>