Is there some reason to not create a new document based on the template? That is how templates are intended to be used. You could open the normal template and import your styles there, but that seems a bit like overkill.

See also:

1. Letterhead AddIn(s) - Default New Document
2. Templates in Microsoft Word
3. Understanding Styles in Microsoft Word
4. Normal Template in Microsoft Word - How to Find or Open the Normal Template