Not if you're upgrading from Windows 10—that's free.
If you're installing fresh, you can also choose to install Windows 11 without a key and later register it to your Microsoft account, which will automatically pull in your Windows 10 credentials. Easy.
Or you could even try out Windows 11 without activating it for a while, if you don't mind the watermark and not being able to personalize the look and feel. If you do go ahead and install, enjoy being on the cutting edge—we'll have a lot more to say about Windows 11 as we dig deeper into the operating system.