The tasks of the vice-proconsul involves assisting the Proconsul in the actual day-to-day running of the Imperial Romulan Senate as well as handle any of the minor details the proconsul may not have time to deal with personally. Though some vice-proconsuls are quite content to serve in a secondary role, a majority of them see the office as a step toward becoming proconsul themselves. This means that many proconsuls have served as vice-proconsul in their time, and the job makes a traditional stepping stone to the highest office in the Senate.
In the case where a vice-proconsul belongs to a different coalition than the proconsul, the position serves an additional purpose which is to keep watch on the proconsul and keep them in check. At the sametime, they look out for the interests of their own coalition in order to ensure that the proconsul does not compromise the coalitions standings. These arrangements typically happen when two coalitions for an alliance and share power in the Senate where they work to shut out the smaller coalitions. (LUG reference: The Way of D'era: The Romulan Star Empire)