Theme changes not being pushed to site

I’m trying to alter the header.php and footer.php but after saving my changes, the alterations are not showing up on the live site.

Is there anything I need to do to push these changes live?

Nope, changes are reflected immediately. Even browser caching is usually not a problem for those kinds of changes because the PHP-generated content generally isn’t cached. You could have some server-side caching setup going on but that’s usually not the case.