The Consensus is the ruling body of the City. Formed at the end of the Faction Wars, the Consensus is an alliance of the City's factions with the Vanguard. Only certain factions are allowed in the Consensus; the former faction Concordat were ejected when they attempted a coup against the Speaker. Others are permitted in by the Consensus's approval. The Consensus allows factions to pursue their agendas through legal, civil channels. The Speaker acts as the head of the Consensus, with each faction and Vanguard order having one representative.
Following the Red War and the death of the Speaker, Commander Zavala became the acting head of the Consensus while its members worked to create a system to elect a new Speaker to become the leader of the Consensus.
It remains to be seen how the Speaker's demise will affect the politics and power balance of the Consensus and, by extension, the City. While the Speaker seemed to lead in a fairly hands-off manner, his loss has still left a substantial power vacuum. As no succession plan appears to be in place, increased political instability and infighting certainly seem possible.
Zavala now seems to be the most powerful individual in the City and the de facto leader of the Consensus, but he seems unwilling to outright replace the Speaker or otherwise accrue power beyond his existing position as Vanguard Commander. Whether or not such a solution will be stable is uncertain, but it seems likely that without a Speaker as a clear leader and mediator, the relative power of the Factions in City politics will increase. This may or may not lead to attempts by the Factions (or the Vanguard) to exert more direct control.
It is also unclear what (if any) position Suraya Hawthorne now has on the Consensus. She does not seem to enjoy formal membership, and given her history and outlook, might not even be interested in it. However, the civilians of the City (particularly those not aligned with a Faction) seem to view her as a voice for their concerns, and the Guardians respect her for her role in the Red War. This gives her significant influence and, assuming she decides to embrace it, may see her become a leadership figure in the City.