With Bruce Harrell currently serving as Mayor, that poses an interesting question: who’s Council President? Answer: Lorena Gonzalez. Because there’s a plan for that.
On January 5, 2016, the day that the current Council members were sworn into office (except Gonzalez, who had been sworn in the previous November, right after the election, to fill an empty seat vacated by Sally Clark), the first order of business was to elect a Council President, and Harrell was selected by his colleagues to serve. The second order of business was to pass a set of routine administrative resolutions, establishing committees, appointing Council members to outside commissions, etc. One of those resolutions set a monthly schedule for who would serve as President pro tem in the event that Harrell was unavailable: travelling, ill, on vacation, or anything else that took him away from his duties in City Hall.
According to that schedule, this month it’s Gonzalez’s turn to serve as President pro tem as necessary. So she’s the boss now.
If Harrell declines to continue to serve as Mayor tomorrow, then he’ll retake his Council seat and once again become Council President. If he does opt to continue, then electing a new Council President is one more task the Council will need to deal with next week, along with appointing a different Council member to take over as Mayor, and then appointing someone to fill the vacant Council seat that would create.
And if they don’t get around to electing a new Council President by the end of the month, then on October 1st Lisa Herbold would become President pro tem. Of course, it’s very unlikely to take them that long, assuming they need to do it at all.
By the way, there’s one other hole in the City Charter’s instructions for handling a Mayoral vacancy: assuming Harrell officially declines to continue as Mayor, it’s unclear when he actually stops being Mayor: immediately, at the end of his 5-day decision period, or when the Council appoints a new Mayor. For that matter, it doesn’t specify when Harrell’s 5-day decision period started: when the Mayor announced his resignation, when that resignation became effective, or when Harrell was sworn into office (granted, the last two were only about two minutes apart, but it’s precedent for future cases).
The staff of the City Attorney’s office should feel pretty good about their job security right now.