Probably not. I say probably because very occasionally it will work. But your new pc will have a different motherboard etc and Windows, more often than not, will detect that. Some of the drivers may not work on your new machine and Windows may not be able find replacement drivers. Also the licence will not activate. A non-activated Win 10 computer is not the end of the world unless you want to make it pretty with themes etc. Much better to download the free ISO tool from here:- https://www.microsoft.com/en-gb/software-download/windows10 and make a dvd or usb flash drive to install a fresh copy of Windows. You should have all your personal files backed up to somewhere else because they will be lost after the re-install. Personal programs will also go but you should have the installation media for those.
As I say make sure that everything you want to keep is backed up to somewhere other than the disk you want install Windows on to otherwise all that stuff will be lost.
Like above that is not the ideal way of doing it. However if you know the motherboard, graphics card and anything else that will require a driver you can pre download these and put on that hard drive and install when you have moved
A License Can Only Be Installed on One PC at a Time
That's Microsoft's rule. So, while you may be able to move a license to another PC, you're supposed to remove it from the first PC before you do that. You can do that by wiping the PC's hard drive or even uninstalling the key from your Windowssystem.
I've done it loads sometimes it will boot other times not. If it does boot all drivers etc will be replaced/installed automatically. You will have to re-register Windows with a key from the new machine or a new key.