I'm going to take a stab at this.
There is some important missing information in your question. Which edition of Windows 10 did you install?
Windows 10 will automatically activate using a digital entitlement that is stored on Microsoft's servers and it is recognized as belonging to your system by a hash of various hardware and software components. It is one of the nice new features about Windows 10 that eliminates keeping track of the product key. https://support.microsoft.com/en-us/help/12440/windows-10-activation
But, it won't automatically change editions. Instead, if Windows can find a matching digital entitlement, or a product key in the BIOS, it will activate with that. Otherwise, Windows will require you to enter a product key matching the edition of Windows that was installed. You need to re-install with the proper edition.
I'm assuming you downloaded your .iso using the Windows Media Creation Tool? If not, download it and use it so you have a proper Windows setup disk or usb drive: https://www.microsoft.com/en-us/software-download/windows10
If you follow the instructions below and Windows setup doesn't ask you which edition of Windows to install at Step 3, then you probably have a product key embedded in your BIOS. Here are instructions on how to modify the installation media so it will always prompt you for what edition of windows to install (thanks to Daniel B for pointing this out): http://www.intowindows.com/how-to-select-pro-edition-while-installing-windows-10/
To install with pro (or home):
- Boot the newly created disc or usb drive you made for Windows 10
- When you are prompted to enter a product key choose,"I don't have a product key." You might not see this step if you have an embedded product key in the BIOS.
- Next, you will be asked to choose which edition of Windows to install. Choose 'Professional' edition. If you don't see this, then modify your installation media as posted above.
- Complete the installation, Windows will automatically activate with it's digital entitlement if this same hardware has previously been activated with Windows 10 Pro.
This is how Windows works, and I'm confident Windows will activate automatically. However, if necessary, after being sure you installed Windows Pro (instead of home like you have), you can activate by entering any previous Windows 7 Pro, Windows 8 Pro, or Windows 10 Pro (even refurb) license key. Sometimes stickers for older license keys are still present on refurbished computers. As of the date of this posting, yes, you can still upgrade for FREE from a previous OS to Windows 10, and that will likely never change.
Changing only the hard drive will not impact Windows digital entitlement validity.