For Mayor Eric Adams, the challenge of leading New York City has taken on an almost absurd quality, with his administration peppered in recent weeks by a half-dozen significant resignations, four federal investigations and two federal indictments, including one against the mayor.

Two of his deputy mayors and his police commissioner have resigned. His schools chancellor was just replaced. And he withdrew his pick for the city’s top lawyer when it became clear that the City Council would reject him.

With the flood of departures and chaos leaving a considerable vacuum at the top of City Hall, Mr. Adams must now rely on a flurry of new appointees and promotions to keep a complex bureaucracy running.

Earlier this week, Mr. Adams elevated Maria Torres-Springer, a veteran civil servant, to become his new first deputy mayor. She and three other highly respected women in the administration — Camille Joseph Varlack, the mayor’s chief of staff; Meera Joshi, the deputy mayor for operations; and Anne Williams-Isom, the deputy mayor for health and human services — are expected to largely oversee City Hall’s key administrative responsibilities.

Of them, Ms. Torres-Springer will play the most critical role in the coming months, handling daily operations across a vast bureaucracy of roughly 300,000 city workers with a $100 billion annual budget.

Her promotion seemed to signal a shift from the cronyism that had typified many of Mr. Adams’s significant hires, and was celebrated by a range of civic leaders, including the Rev. Al Sharpton; Kathryn Wylde, the leader of a business group; and progressive officials including Chi Ossé, a City Council member who has urged Mr. Adams to resign.