I'm a little confused about which is the 'new one' and are there 2 'new ones'...
Loading an OS usually requires reference to ther hardware that is part of the system - type of processor, type of chipsets, type of usb controller, etc.
It may be possible to pop in a hd that has on OS loaded while in another system, reboot several times while the OS tries to find all the new devices, and pray, but I would not recommend it.
You could clone your laptop hardisk to a new laptop hd, then replace the original with the new one since it is now a clone (it can have more capacity and be faster than the original...)