ESO has 7 playable Classes, and with Update 46 implementing Subclassing, it's now even less likely that we'll see an 8th Class.
For starters, here's a promotional image showcasing the 7 Classes using the Class Sets in the Infinite Archive:

(pictured left to right: Necromancer, Warden, Templar, Arcanist, Sorcerer, Dragonknight, and Nightblade)
If a new Class would be added, that would entail adding the same number of Class Sets to the 8th Class as well as creating a new motif. It's unlikely, but still doable.
Now, here's what the new "Class Master of the Second Era" achievement looks like:

The description reads: "Prove your mastery of Second Era martial and magical disciplines by completing the achievements listed below."
If a new Class would be added, would it be added to this list? If so, that would require updating the icon. What would happen to players who earned this achievement before additional requirements would be added to it? To avoid that problem, would the new Class Mastery achievement be in a separate Achievement? If so, then it wouldn't be listed as one of these Second Era martial and magical disciplines. This achievement implies that these 7 Classes are
the only martial and magical disciplines of this Era, so it wouldn't make sense to have any more than these.
Finally, here's what the quest NPC for Subclassing has to say regarding the kinds of Classes you can pick:

There are three broad categories: the study of the high arcane, the duality of light and dark, and the powers of the natural world. In those categories, the eligible Classes are directly referenced by name.
If a new Class would be added, then it would invariably require the voice actress to record new voice lines to accommodate the new options. While you could fit a new Class into one of the three broad categories, the dialogue within those categories would have to specify the new Class by name. If, instead, a new broad category was made to avoid that problem, then the dialogue describing the broad categories would need to be updated to include the new broad category.
This is why I think we will never get another Class in ESO. We may get new Skill Lines (akin to how we got the Psijic Order Skill Line rather than a Psijic Order Class) but I think the way things are structured in various areas of the game imply that adding an 8th Class is infeasible. There is a finality to how the 7 Classes are presented as
the playable Classes, and I don't think anything will change that.
PC/NA — Lone Werewolf, the EP Templar Khajiit Werewolf
Werewolf Should be Allowed to Sneak
Please give us Werewolf
Skill Styles (for customizing our fur color),
Grimoires/Scribing skills (to fill in the holes in our builds), and
Companions (to transform with).