Now that Tera is finally here to stay (God bless us), two main threats remain, and will probably be on the next radar.
Honorable mentions:
Before that, honorable mention to, first off Annihilape

and Dragapult

, then Iron Valiant

, Garganacl

, Gholdengo

, Volcarona

and Dragonite

.
For the last five, while I think some discussion and maybe proper testing down the line might be a due, they're currently not a fundamental problem. Although I'd like to point out that I'm convinced a lot of people seem to undervaluate Garganacl intentionally, as to keep using this strong as F monster.
For the first two, they're definitely third and fourth in threat order, but are in need of an analysis after the ban of the other two Pokémon I'll present in a sec. I think we need to observe how the metagame, and thus Tera playable on them, evolves, to assess action being taken on them. But it's a 75% probability of action at worse for them.
EDIT: Also a Shed Tail/Cyclizar

ban would fix a lot of the 'setup' problems, mostly Volc/Dnite, but also some Hands, Valiant, Quaqua or Garga comps, which abuse heavily on this setup assist to devastate defensive COREs. Altough that would come after Pult imo, in fifth place.
The tier-'ruining' problems:
No no no, we need to talk about the two real big guns from now on.
Chi-Yu

is broken, okay, we got it. I admit that it is really overwhelming in the builder, in-game not as much if you make the right calls to limit it in its actions. Still, a bit less than broken doesn't make you healthy.
Chien Pao

on the other end, is sooooo underrated as a banworthy Pokémon imo. I don't know how people keep calling it normal, when this Ice-Tera'd thing has no current SI with CB/LO. I may be hella biased because the team I ran to achieve requs was not what you'd call the best matchup against this exact set of CB Tera-Ice, but it definitely seems quite heavily broken, and I think it deserves the most attention after Chi-Yu, not the ridiculous Ape which can '''at least be checked with Special Attacker or be outsped''', if I'm being a bit hypocritical here. Pao is so damn fast it's ridiculous, seriously.
I'll continue to check on this thread as things go on, and will maybe make a few other comments.
TLDR: Tera kept is incredible, Ape and Flying Lizard need to wait until we ban two other things first, Shed Tail/Cycli should probably follow, Valiant/Salt/Ghold/Volc/ExtremeKiller2.0. need further investigation, and Goldfish/White Panther should be booted out.