Even if the hardware is compatible, the operating system installation will not be.  At minimum, it'll trip an activation request (which Microsoft won't permit;  the OEM license is permanently tied to the original system).  More likely, the drive won't fully boot -- and even if it does, the odds of ending up with a stable, functioning install of Windows are low.  
I'm trying to help a friend with her new computer.  She'd like for me to put her old hdd into the new computer and boot from it.  It is Win 8 but I can easily update it to win 10.  Is this a possibility?
install old hdd to new computer.