Coming from the security aspect, I would personally, and professionally, advise you to avoid fingerprint scanning security. The technology has been easily hacked a number of times at various hacking conventions, as well as all over the internet. If you have an alternative, I'd recommend using it. So far, fingerprint-based biometric verification is quite poor for security, and it's unlikely it will get much better any time soon. Just being upfront, since security has been a huge hobby of mine for years.
With that said, if the reader currently is functional with your laptop right now, and you're using a different version of Windows, there's a good chance the hardware will work on Win10. Will there be a driver available, though? That's a great question. I'd recommend checking on the HP website, and seeing if your computer has any drivers available for Win10. If you can't find any valid drivers, you could try using IObit Driver Booster 2 to obtain a driver. So far, that has been the best solution to solving my driver problems, and I'm currently using their Pro version, as the free version is absolute shyte for download speeds (capped around 100 kB/s).
That's about all I can really say. As eatmypie mentioned, it's unlikely another driver will be written if it's an older piece of hardware, and they've made their share of profit from it. Usually, older hardware will have some sort of compatibility with the next gen OS, but it's up to the companies who made the hardware to release drivers at that point. If you can find the specs for the fingerprint reader/scanner, see if they have any drivers for Win10.