Show Taxonomy Child Terms (name and image) on Parent Term Page

You can try this.

$parent_terms = get_terms( array(
    'taxonomy'   => 'post_tag',
    'hide_empty' => false,
) );

foreach ( $parent_terms as $terms) {
      $term = get_terms(array(
        'taxonomy'   => 'post_tag',
        'hide_empty' => false,
        'parent'     => $terms->term_id
      ) );
      foreach ($term as $term_child){
         $string .= '<li><a href="' . get_term_link( $term_child->term_id ) . 
                     '">' . $term_child->name . '</a></li>';
      }
}

return $string;