You wouldn’t have to change your site. You could add a php powered gallery on your hosting without issue and link to it from your html pages.
Granted, You can make html pages and name the file a php page and it would have no effect on how the page loads.
For example, you could make an sample.html file, put all your html in it, and then rename it sample.php and sample.php would then load without issue in your web browser. Try it if you want
A popular and tried solution is Gallery by Menalto http://gallery.menalto.com/
It’s likely available in your hosting control panel if your provider uses cPanel under Fantastico” which is a popular option for easy quick installs for most hosting providers.
4images is another popular easy gallery, http://www.4homepages.de/
http://www.plogger.org/ is pretty lightweight.
http://phpimagegallery.com/ is a pure php that is usually easy to integrate.
I hope this helps! If you have any questions just ask away