battlemage

Actually dragonknights, templars and wardens are new to TES lore, introduced by Zenimax for ESO. In ESO, classes are technically different types of mages. Whereas previous TES game classes defined a broader range of specialities, based on a trade or profession of some kind, and nearly all magic was learnt under 5-7 schools, which are usually defined by their application rather than their means. That said, when we talked about "mages" in previous TES games, that typically referred people who could use just about all those schools and used little but spells.

We already have the skills to play most old style classes. Magic skills are mostly covered by class skills, staff skills, Mages Guild, light armor, Psijic Order and scrying. Combat skills are covered by weapon and armor skills. Stealth has less use in ESO than moin some TES games, but a lot of it falls under legerdemain, medium armor, Thieves Guild, Dark Brotherhood and "speechcraft" awkwardly being two starting passive perks for the Mages Guild and Fighters Guild.

Acrobats and monks are less playable in ESO. All player characters jump the same distance and can only climb ladders that work like doors mechanically. We don't really want one class to get to places where others can't (although nightblades already can, using teleportation spells).

A problem for monks is that they'd have balance using no weapons or a perhaps melee staff with everyone else who does use weapons. I wonder if there's an opportunity to make a hand to hand combat skill that also serves as an alternative for staff users. So the stamina morphs would be used by monks and the magicka morphs would be used by magicka players who are fed up of staves. In that case, it couldn't be unique to one class. Although I'm sure what it would do. Hand to hand in TESIII was used to disable enemies without killing them. Maybe it could be used by tanks to debuff, stun and imobilise.

When I think of other types of magic in existing lore, I think of tongues and sword singers, neither of which would be plausible. My favourite suggestion for a new class is some sort of artificer/combat engineer using Dwarven devices and such.