Can I embed a gallery on my own photography website?

The supported approach is white-label album domains — your albums live at albums.yourstudio.com, which from a visitor's perspective is as close to embedded as most clients need. If you're picturing an actual iframe sitting inside a page on your site with your navigation around it, that's not something the platform advertises, so check with support about what's possible before you design your portfolio around it. For most photographers, sending clients to a branded albums subdomain is indistinguishable from an embed anyway.