wp-orderby-termmeta.php

<?php

namespace wp_orderby_termmeta;

add_action( 'posts_fields', __NAMESPACE__ . '\\posts_fields', 10, 2 );
add_action( 'posts_orderby', __NAMESPACE__ . '\\posts_orderby', 10, 2 );

// Append the "sort" column to the query...
function posts_fields( $fields, $query ) {
    if( 'art' == $query->query_vars['post_type'] ) {
        global $wpdb;
        $fields .= ', IFNULL( ( SELECT ' . $wpdb->termmeta . '.meta_value FROM ' . $wpdb->termmeta . ' INNER JOIN ' . $wpdb->terms . ' ON ' . $wpdb->termmeta . '.term_id = ' . $wpdb->terms . '.term_id INNER JOIN ' . $wpdb->term_taxonomy . ' ON ' . $wpdb->terms . '.term_id = ' . $wpdb->term_taxonomy . '.term_id INNER JOIN ' . $wpdb->term_relationships . ' ON ' . $wpdb->term_taxonomy . '.term_taxonomy_id = ' . $wpdb->term_relationships . '.term_taxonomy_id WHERE ' . $wpdb->term_relationships . '.object_id = ' . $wpdb->posts . '.ID AND ' . $wpdb->termmeta . '.meta_key = "sort" AND ' . $wpdb->term_taxonomy . '.taxonomy = "art_type" LIMIT 1), 0) AS `sort` ' ;
    }
    return $fields;
}

// ... then, sort by it.
function posts_orderby( $orderby, $query ) {
    if( 'art' == $query->query_vars['post_type'] ) {
        $orderby = '`sort` ASC, ' . $orderby;
    }
    return $orderby;
}