Probably, some of the scripts on the page call "http" instead of "https" and I found several just viewing the source code now.
A quick solution is to add a fix in the [.htacess] file that uses mod_rewrite with a regex to convert all [http] links to [https].
Then do a crawl through the code that generates each page for display on Tavern and change the view controller to replace any instance of [http] to become [https].
If the Tavern uses a database to store content, you can also do an SQL update for all tables that store the [http] content and convert those to [https] also using regex select then update MySQL commands (if that is your database engine).
This will work on all locally hosted content on the [gamingtavern.eu] domain, but may break some external links like photos, but worth the effort to keep the Tavern secure.
I do not know the architecture behind the Tavern, but most modern Content Management Systems have a Model-View-Controller (MVC) architecture, so they can translate into other languages too. Like with Drupal and WordPress, you can change the View Controller to alter all [http] into [https] before it renders the page, even if the database text content has [http] saved.