The W7 installation on the old computer will be "tied" to the hardware on that machine and would be unlikely to work with the hardware on the new machine
Technically this is more likely to be possible than not. As long as the old disk is SATA (and not PATA) then Windows will sort itself out - provided you can supply all the drivers for the new hardware. I have done this several times, even moving from intel to AMD or vice-versa.
If you are going to try this, I would remove or disable your Win 10 boot disk first to ensure that you don't inadvertently screw that up!
PJD1 is quite right about the licensing problem, though. Unless it was a full retail version of Windows 7 (i.e. not an OEM license that came with the PC), which is fully transferable, you can't (legally) use the licence on a different PC.
If your licence allows it and you want to go ahead, you can do a "sort-of" dual-boot by simply changing the HDD boot order in the BIOS - not as clean as having a boot menu option, but saves re-installing one or other of the existing OS installations.
SD