New Hard Drive Windows 7 Install

I have Toshiba Satellite laptop and my hard drive crapped out on me, when I turn it on the hard drive starts clicking and that’s about as far as it goes. I’m planning on buying a replacement hard drive, an exact replacement, no upgrades but the computer didn’t come with a Windows 7 disk. I have the Windows 7 product key and that’s it. If I pop in the new hard drive will the product key be enough to reinstall windows or is there more I need to do? Thanks.