If you're on regular PC, you can redeem the Gold key on your existing ESO account page and it will upgrade. The same goes for Morrowind too. Works perfectly.

It also works for ESO accounts created through Steam, but the caveat is that you need at least the base game (Tamriel Unlimited) purchased on Steam to play those accounts. You also can only play those accounts through the Steam client - it will not let you play through the regular PC client (you can circumvent this if you have a regular PC account and you link it to your Steam copy of ESO - doing it this way actually lets you play through both clients).

To simplify:

On regular PC -> Redeem key on ESO account page -> Good to go

On Steam (or ESO account created through Steam) -> Have at least base game purchased on Steam -> Redeem key on ESO account page -> Play through Steam client -> Good to go