Change link to gallery

imajica

If I set a gallery to be visible to anyone with a link... is there a way to reset the link at a later date, so that I can keep the gallery in place, but block anyone who had a link in the past? I know I can probably go to site settings/basics and change the Custom URL... but without doing that, I notice that there are random characters in the URL after the site gallery name. Can something be done so that part of the URL changes?