No extra steps are needed when you move a drive from one Mac that's compatible with the new Mac other than opening Disk Utility and partitioning / erasing the drive.
If you have tried that several times and get the same hardware error - it's now time to repair the new system by triaging the issues:
- Reconnect all cables and retry
- Put another working drive back in the new Mac and test
Either the Mac is now broken or the drive now is broken or the cabling is now broken. A repair will tell you which of the three above happened.
For this reason, I almost always connect the new hard drive externally over USB and make sure the old Mac can boot from the new drive and work out any installation issues. Only when I'm convinced I have the correct OS to boot an external drive do I remove it from the external sled and do the swap.
Much faster to know the repair went well in that case but you do need a USB to SATA (or whatever your SSD / storage connection is if you're not working on a 2012 era MacBook).