A "council speaker" is someone who leads discussions and manages meetings within a council or similar governing body. They make sure everyone has a chance to speak and that meetings run smoothly. Full definition
The city council speaker is not elected by voters, but is selected by the 51 members of the city council without any direct role for the public. (newyorktrue.com)
She will inevitably be asked the same question as every other council speaker: will you run for mayor? (observer.com)
The series of public forums is unprecedented for selection of the city council speaker. (newyorktrue.com)