I tend to picture the Romulan Star Empire as being something akin to 18th Century Britain.
A mostly -- but not entirely -- ceremonial Emperor, with a Senate comprised of both noble families and commoners, but with the noblemen invariably gaining more power and prestige, inheriting their seats whilst the commoners in the Senate compete for popular votes. The DS9 episode "Inter Arma Enim Silent Leges
" implied that one ascends to the position of Praetor with a vote of the Continuing Committee; I would take that as meaning that a Romulan seeking to become Praetor would be trying to cultivate alliances with powerful Senators and Continuing Committee members. Presumably the position is ceremonially appointed by the Emperor on the basis of the Continuing Committee's vote.
The Tal Shiar would likely make up the fifth basic power bloc in the Star Empire. Whether they're a partisan organization, or one that ruthlessly puts down dissent against the Praetor of the day, whomever that Praetor might be, I don't know. I would tend to infer that they seek their own agenda, independently of the Senators, Praetor, and Emperor, though they have to curb their behavior and always have a rhetorical justification for it that seems non-partisan.