Jedi Council is nothing but a vaguely-referred-to NPC group this timeline, at least right now, and I have no intentions of changing that. The closest you'll have to a council would be speaking to the Lord and his generals.
In regards to an Order ICly led by the Jedi Council:
In an open galaxy, it's extremely restrictive and almost illogical that a Jedi would be told to direct their queries to the Jedi Lord and his generals when the Council is what the Order revolves around - war or not. Please reconsider how this can work this era, or at least how these NPC's can be contacted? @Elijah Brockway
Agreed Asinine. A council would be great, I would need some more detail of the NPC's for my two characters as well, as one was already mentioning the council x3
Second, in case you didn't read the write-ups in the Jedi Faction board, the Jedi PCs are not the entire order. They're part of the Army of Knights, led by the Jedi Lord and his generals. Separate from the rest of the Order, and not revolving completely around what the council says.
Considering how, after all, the Council didn't want to commit the entirety of the Jedi Order to going after the Sith and didn't want to be proactive. So originally, Bau Zo had their tacit approval to make his army (which the PCs are part of) and go out and do that whole fight-the-Sith thing.
So, no, considering how the part of the Jedi order that PCs are a part of is set-up and how things are written up, it's not that illogical at all. If your character chose to be part of the Jedi Army - which is assumed by the fact that they're a PC in the Jedi faction - then they also chose to separate themselves from the rest of the order.
They answer to the Jedi Lord and his generals, they get missions and commands from the Jedi Lord and his generals, and if they have to talk about something, they take it to the Jedi Lord and his generals. That's how it's been since timeline start and that's how it's going to stay for the foreseeable future.