So of the founding members, that leaves us with one where we don't know its basic constitutional framework -- Tellar! All we really know about them is that their state is known as the United Planets of Tellar (A Choice of Futures, Tower of Babel). Are they led by a President? Governor? Prime Minister? Chancellor? Minister for the General Administration of the Cabinet? Elder of the State? Minister-President? Sultan? Statsminister? Chief Magistrate? Taoiseach?
The
Gateways series mentions an historical
High Councillor to the First Seat of Tellar. When the Tellarites were forming their first true world government, Ger, the current (the first?) High Councillor accepted the colAndor Scrolls from Andorian delegates, which were to serve (so the Andorians intended) as inspiration on how to make such a government function (my personal "headcanon" is that Thalisar the Last wrote these

). Ger later refused to give them back, saying that they'd been a gift, and he kicked the Andorians offworld. Things were sour after that. (It's not explained whether the Tellarites truly thought the Andorians were being two-faced in wanting them back, or whether this was just an excuse to start a
really big argument, IE. the Tellarites were being Civil and the Andorians misread it as true hostility).
A bit obscure as regards the current continuity, but I've always liked it as a reason for initial cool feelings between Andorian and Tellarite.
http://memory-beta.wikia.com/wiki/ColAndor_Scrolls
In the modern era,
SCE insists that the name of the Tellarite head of state is near-impossible for Humans to pronounce (in the original Tellarite, I assume).
How about:
Big Cheese of Tellar Prime?