What happens if NYC Mayor Eric Adams resigns or leaves office?

NEW YORK — The indictment of New York City Mayor Eric Adams, raises questions about the future of city leadership. Sources told CBS News New York Wednesday night that the indictment followed a federal investigation. Now, despite multiple calls for his resignation, Adams is showing no sign he plans to step aside.
While investigations have swirled around Adams and several of his top administration officials for months, Adams has remained defiant. When asked if he would consider resigning earlier this week, he replied he was “stepping up, not stepping down.” 
“A year from now, I see myself again raising my right hand and being called the mayor of the city of New York,” Adams said. 
But what happens if Adams either does resign or is removed from office, which Gov. Kathy Hochul has the power to do? Two other mayors have previously resigned: James Walker, in 1932, and William O’Dwyer, in 1950. No New York governor has ever used their power to remove the mayor, to date. 
Hofstra University law professor James Sample told CBS News New York the state has seen its share of corruption investigations over the years, “but none of those people were the mayor of America’s largest city,” adding, “the pressure will be immense.”
“He’s got to take care of himself, he’s got to work on his defense here. These are potentially very serious charges — we don’t know the details of them yet, until the indictment is unsealed — but it’s going to be very hard for him to survive, politically,” Sample said.
According to the New York City Charter, if the mayor leaves office, the next in the line of succession is the public advocate. That position is currently held by Jumaane Williams. After that, it’s the comptroller. That office is held by Brad Lander. 
In this case, if Adams did resign or otherwise left office before his term was up, Williams would become mayor. Lander would only take office as mayor if Williams and Adams were both not in office. 
However, if either the public advocate or comptroller became mayor under those circumstances, they would not have the power to appoint or remove other mayoral appointees from office. They also would not be able to sign, approve or veto any local law for nine days. 
The acting mayor would have three days to set the date for a special election, which would have to be held within 80 days.