Installed new SSD now old storage HDD not appearing

Please make sure you bring it "online" in disk management.
Go to left-hand side, where it does show up in disk management, as Disk 0 or Disk 1, and make sure it shows "online" as the status.

If it shows offline, then right-click that left-most panel and choose "online."
Sorry if that's a 'basic' answer, but you didn't give much info.

You did say it shows up in Disk Management - I hope that is correct, vs. "Device Manager."

Also, please double-check for any existing "drive letter" conflicts from before you moved to the SSD device - i.e., if you forget to re-allocate your old external storage device to a NEW logical drive letter, like G: or H:, for example, then it could be that your new SSD or some other device might try to claim the logical drive letter that was previously being used by the old storage device that you are trying to view.

I have had that happen to me before, and it was puzzling to figure out.

Please update us and let us know what your ultimate resolution is, or if any of these tips help you, please acknowledge and let us know. Thanks.