You create a new document based on a template you do not save the template as a document. [This is jargon, but an important distinction.] This was my suggestion in my previous response. Try it.

The links, though, were not for show. The first explains what templates are and how to use them. Templates may contain numerous features, not only headers and footers. Yours may not contain those.
The second link clarifies what goes from a template and stays in a document. It also talks about what happens when you attach a different template to an existing document (it does not change existing header footer content).

I encourage you to read the linked articles, including those on styles. If you are going to be working with Word for your job, you need to more.
You could start here: Basic Concepts of Microsoft Word - from Shauna Kelly