update_post_meta

function add_appcat_automatically($post_ID) {
	global $wpdb;
	$thispost = get_post($post_ID);
	$post_slug = $thispost->post_name;

	if(!wp_is_post_revision($post_ID)) {
		$app_parent = get_option('app_brom');
		$app_name = get_the_title($post_ID);
		$new_term = wp_insert_term( $app_name, 'product_category', $args = array('parent' => $app_parent) );

		if ($new_term instanceof WP_Error) {
		} else {
			$new_term_id = $new_term['term_id'];
//Everything works till this point and $new_term_id gets correct value

			update_post_meta($post_ID , '_app_cat_id' , 'blue');
//This does not work. Will change 'blue' to $new_term_id
		}
	}
}
add_action('publish_applications', 'add_appcat_automatically');