A Consul was a diplomatic or political title and position.
In the Romulan Senate, a Consul was a high position. The head of each of the major coalitions within the Senate holds the office of Consul. A consul speaks for his coalition, serves as the public leader of the coalition, and represents the coalition on the Continuing Committee. Being a consul is a position of considerable public exposure, and consuls are often targets for political schemes aimed at their coalitions, since weakening the consul tends to weaken the position of the coalition as well.
A consul who suffers such a loss of influence is expected to resign for the good of the coalition, and coalitions can vote to elect a new consul at any time. Consuls may also exercise other powers, but key governorships and ministries remain in the hands of the consuls of the major coalitions. (Last Unicorn RPG: The Way of D'era: The Romulan Star Empire)