I don't want to see the councilors again. If we're going to another galaxy. let the characters on the ark/ship form their own whatever with who they have and go from there.
Right, but we have to have some sort of government.
The thing about the quarian form of government, at least on board the ships, was that it showed that the military could not rule over its people. This is why the long winded explanations of what her government theoretically was supposed to do, but in actuality was much different.
The same could be said true of the Ark. This is assuming that we do not have Cryo-sleep as an option. The military can rule, but only for a short period of time. Then it will shift back to what they are familiar with.
Now, assuming that we do have Cryo-sleep and are talking about colonies in Andromeda? That paints a whole 'nother picture. Colonies in Andromeda would have no place even for a central government unless they designate a planet to be their central government. Or, they designate the Tempest to be the new Citadel. However, since they don't know which colonies will "take off" in terms of economic, military, and political power.... That would be kind'a pointless.
As a matter of fact, I'll bet that's what they do. Decide that the Tempest is now the de facto Citadel and make all decisions from there. This would give them a home base starting point... And a place where all decisions can be made.
We might have a different form of government, just like the quarians did. But I really don't think so. I think it will be just more of the same. A council to represent all races. Not just the three (or four) major races.