Only show posts with a specific term of an associated taxonomy in a custom post type archive

I have a custom post type “movie” with a taxonomy “period”. The “period” taxonomy has two terms: “current” and “past”.

Is it possible to only show posts with the “current” term in the “movies” archive page (archive-movie.php)? If so, how?
I’ve used the template_include filter before to show templates conditionally, but I’m not sure if this hook is useful in this case.

Any ideas?