Depends on what Windows you have.
If you have a Windows 10 that you bought retail *or* a previous Windows that you updated to Windows 10, so long as you've connected it to a Microsoft account, you ought to be able to continue using your license. If this was a Windows from a prebuilt PC or an OEM version of an older Windows version, you'll likely have to repurchase.
As for reinstall, you always should reinstall when making significant changes. OS installs are not intended for, or designed to be, modular parts that you just throw into new builds. Sometimes it'll work, sometimes it won't, and sometimes it will work and you'll be hunting down weird problems for months, but it's always best practice to do a full, fresh install on a new or updated build.