Activate Publishing Infrastructure to make it work. Click on Site Actions > Site Settings > Site Collection Features to find it. (You need to be a Site Collection Administrator to do this).
We need this anyway because you get the Navigation link back which allows you to open Quick Launch menu items in a new window and to do Audience Targeting on menu links. (It does make the modern Quick Launch go a bit weird when you try and edit it, but it doesn’t matter, you just need to click Edit on that twice to make it work again, no showstopper there).
Then go to the list or library you want saved, click on List / Library Settings, (notice that the Settings menu has changed….).
Add the name and description. Only include content if you want the documents or list items themselves added – you would rarely do this, only in the case of moving a full library to another location. The size limit of templates is 10MB. Click OK.
The list is added. Click OK.
To use the template, click on Add an App from the Settings menu, and either search for it, or sort the apps by name and scroll to find it.
To manage templates, go back to Site Settings > List Templates.
The default view is pretty useless, so modify it to show the fields that make sense to you. Select the template you want, then either click and select download, or use the download option on the Files tab on the ribbon. It will download as a .stp file.
Go to the site collection where you want to leverage it, go back to Site Actions > Site Settings > List Templates, then click on Upload from the Files tab. The template will then be available in the new site collection.
Please just keep governance in mind here, delete templates no longer needed because they will be available to every single edit rights user on the site collection. Keep the list clean. And don’t make the mistake of saving a management minutes library, include the content full of confidential minutes, and roll it out to every single site in the company. We’ve seen it happen…