If you had "everyone" permissions on the files/folders on the drive on the old server, they will be the same when the drive is in the new system.
If you had specific user permissions, UserA, that user is given a serial number called a "SID". After moving the drive, when you look at the permissions for the files/folders you will see the old UserA as a long strng of numbers. That is the permissions from the old server.
If you created a UserA on the new system before moving the drive, you just need to apply permissions for that user to the files/folders on the drive once the drive is installed, and delete the old permissions for the old UserA