Get one custom taxonomy category

Your logic looks to me like it boils down to “if union is selected, then echo a link to union, else do nothing.” I think your description is much too complicated. It looks like you can effectively ignore paid completely.

function wpv_check_for_union_func($attr,$content="") {
  global $post;
  $taxonomy = 'yourtaxslug';

  $union = has_term('union', $taxonomy, $post);

  if ($union) {
    $term_link = get_term_link( 'union', $taxonomy );
    if( !is_wp_error( $term_link ) ) {
      return '<a href="' . $term_link . '">union</a>';
    }
  }

}

add_shortcode( 'wpv_check_for_union', 'wpv_check_for_union_func' );