Once the repo is transferred, the Pages site belongs to the new owner. The old URL https://<olduser>.github.io/<repo> either 301-redirects to https://<newowner>.github.io/<repo>, or it stops resolving, depending on how GitHub handled the transfer. You don't have a switch on your side to turn it off anymore because you're no longer the repo admin.

A few things you can actually do:

• Ask the new owner to unpublish the site. In their repo: Settings → Pages → on the right side there's an Unpublish site button (if Pages is enabled), or they can set Source to None. That kills the URL entirely.
• If you still have admin on the transferred repo (rare after a transfer), you can do the same from your end. Worth checking your access level, the transfer sometimes leaves you as a collaborator.
• Get the new owner to delete the whole repo if they're not using it. That removes the Pages site in the same move.

For the indexing side (which is what usually matters most):

• If you own the old URL in Google Search Console (you registered <olduser>.github.io as a property), you can file a temporary removal request there to drop it from results fast, then let the 301/404 do its job over time.
• Add a <meta name="robots" content="noindex"> tag to the site's pages, but this only works if you can still push to the repo, which circles back to the new owner.
• For a full hard reset, the new owner can add a robots.txt at the root that disallows everything, then request re-crawl.

If the new owner is unresponsive, GitHub support can step in under the content removal policy if there's a real reason (DMCA, personal info, etc.), but "I just don't want it live" usually isn't enough to trigger that.

What's on the site that you need gone? Knowing that might open up a faster path (e.g. DMCA if it's your code/content, GDPR if it has personal info).