Adding external HDD but not showing Volume

Ed_Canada_Ontario I've had this problem before that turned out to be caused by a faulty cable on the enclosure.

Though it might be that the external drive isn't plug and play and needs to be plugged in before the machine is turned on, assuming this wasn't already the case?

In regards to damaging the drive when removing it and installing it in the enclosure, you'd be amazed at how easily damage from static electricity can be caused so it's always a possibility.