The default WordPress installation makes the following clearnet connections that must be eliminated for hidden service operation:
Automatic updates: WordPress checks api.wordpress.org for core, plugin, and theme updates. On a hidden service, this check fails or, worse, could succeed if there is a configuration error that allows clearnet connections. Disable auto-updates in wp-config.php:
define('AUTOMATIC_UPDATER_DISABLED', true);
define('WP_AUTO_UPDATE_CORE', false);
Gravatar images: User avatars load from gravatar.com, an external clearnet service. Disable Gravatar in the Settings > Discussion panel, or use a self-hosted avatar plugin that stores avatars locally. Every Gravatar request leaks the server IP to Automattic's CDN.
Google Fonts: Many WordPress themes load Google Fonts from fonts.googleapis.com. Audit your theme's functions.php for wp_enqueue_style calls referencing googleapis.com and replace with locally-served fonts. The Google Fonts Helper tool (itself a clearnet service accessed separately) can generate self-hosted font packages.