Form to custom post type and custom taxonomy

Use WP set object terms

$new_post = array(
        'post_title'    => $title,
        'post_content'  => $description,
        'tags_input'    => array($tags),
        'post_address'    => array($address),
        'post_status'   => 'draft',           // Choose: publish, preview, future, draft, etc.
        'post_type' => 'trademen'  //'post',page' or use a custom post type if you want to
);
//save the new post
$pid = wp_insert_post($new_post);
 wp_set_object_terms( $pid, $industry, 'trademan-industry' );