sharepoint online – What access is required in order to add Site Collection Content Type Policies Templates

Being quite new to the SharePoint Online environment, I’m having some trouble to find what is the required permissions to add a Content Type Policy Template in a site collection.

When trying to add a new one, I will get the usual “Sorry, you do not have access” when trying to save the policy. The funny part is that I’m an additional administrator for that SharePoint site, and even a colleague with the Global Admin rights could not create a policy. Creating them in a subsite of that site via the library settings works fine though.

Is there really an access issue, or something else which might block the creation of the policy?