If you have a retail version of windows 7 then any updates related to your windows 7 can be installed on any computer as long as you do not have the original Windows 7 or the Windows 10 linked to your windows 10 running on another machine.
in other words, yes you can run Windows ten using your windows 7 key on another machine.
But if you are gong to run windows 10 on the new machine then why bother using your key?
the other problem is that some machines mainly laptops will have the key in the UEFI, so that may confuse the issue
Desktop machine now powered by windows 8.1 pro 64bit, no dreaded metro, laptop by Linux