At Los Angeles City Hall, everything is suddenly up in the air.

With Mayor Eric Garcetti again in the running for a post in the Biden administration — this time as U.S. ambassador to India — politicians, bureaucrats, activists and others are trying to figure out what a mayoral departure would mean for the city and its most pressing issues.

An early exit could reshuffle the race to replace Garcetti in next year’s election. And it would likely trigger another, behind-the-scenes competition for the post of interim mayor — a choice that would be up to the City Council.

“It’s going to have a ripple effect,” said Loyola Law School professor Jessica Levinson, “not just in terms of who Garcetti’s successor would be but how that would affect the race for mayor, who on Garcetti’s staff stays and goes and, perhaps most importantly, what happens to the mayor’s initiatives and goals.”

A White House official confirmed to The Times that Garcetti is on the short list for the overseas post. President Biden’s next batch of ambassador nominees is coming “soon,” a press secretary said earlier this week.

The waiting game has injected a new source of volatility into a government that was just finding stability after a year of upheaval caused by the COVID-19 pandemic. Angelenos have been getting vaccinated in large numbers, and a massive infusion of federal funds has pulled the city back from the financial brink.

But plenty of big issues remain.

Activists who are determined to address police brutality are pressing city leaders to shift funds away from the Los Angeles Police Department toward social services. A federal judge overseeing a massive case on the city and L.A. County’s handling of homelessness recently ordered officials to offer shelter or housing to everyone on skid row by the middle of October — a move the city is fighting in court.

With Garcetti potentially on his way out, some of the most difficult decisions could easily be put off, said political consultant Eric Hacopian.

“It’s a destabilizing thing until he clarifies that he’s going or not going,” he said.

Garcetti, whose term ends in December 2022, was an early supporter of Biden in last year’s presidential race, serving as a co-chair of his campaign committee. Five months ago, Garcetti announced that he had decided not to take an unspecified job in the administration, saying there was “no task more urgent” than remaining as mayor during the peak of the pandemic.

In recent days, however, Garcetti has not publicly ruled out the idea. Meanwhile, his administration is undergoing major changes.

One of the mayor’s longtime advisors, City Administrative Officer Rich Llewellyn, recently announced plans to retire. Garcetti picked a high-level aide, Deputy Chief of Staff Matt Szabo, to replace Llewellyn. At the same time, some of Garcetti’s city commissioners have been wondering whether a departure by the mayor could lead to their ouster.

Outside of City Hall, some critics have suggested they would not be unhappy if the mayor moved on.

Matthew Umhofer, an attorney for the L.A. Alliance for Human Rights, the plaintiff in the federal suit over homelessness, said his clients view Garcetti as less supportive of their goals than some of the council members.

“If there’s a vacuum on the executive side,” he said, “I think it’s highly possible that the legislative side steps in.”

If Garcetti is indeed tapped for a diplomatic post, he would be the first Los Angeles mayor in more than a century to resign partway into his term. The last one to do so was Charles Sebastian, a former police commissioner who stepped down in 1916 after a newspaper published his love letters to his mistress.

Garcetti was first elected mayor in 2013 after serving a dozen years on the City Council. The son of former Dist. Atty. Gil Garcetti, he was re-elected in 2017 to serve an exceptionally long term — 5½ years instead of the usual four — because of a change in election dates.

If he leaves ahead of schedule, the council would have power under the City Charter to appoint an interim replacement to serve out the remainder of his term. Until that decision is made, the council president would serve as acting mayor.

The charter also gives the council the ability to call a special election, rather than waiting until the mayor’s term has run its course. But those types of elections can be expensive unless they are consolidated with other contests, such as the upcoming recall election of Gov. Gavin Newsom.

Complicating matters further, any special election would likely be followed months later by the regularly scheduled city election, which is set for June 2022.

Behind the scenes, a number of candidates have surfaced for interim mayor, including City Council President Nury Martinez, Councilman Paul Krekorian and former City Controller Wendy Greuel. Council members might hesitate to put someone in the interim post if they believe that person would use the role as a springboard for a mayoral campaign.

City Atty. Mike Feuer and Councilman Joe Buscaino have already entered the 2022 mayoral race, and at least four other council members — including Martinez — are weighing the idea.

On Friday, an aide said Martinez intends to govern, not engage in speculation about the future.

“She is focused on making sure our communities have the leadership they deserve — whatever role she is in,” said spokeswoman Sophie Gilchrist.

A Krekorian spokesman said it’s “a little premature to speculate” about a political vacancy that does not yet exist.

“If the need were to arise, as always, I’m sure Councilmember Krekorian would be prepared to serve in whatever capacity best enables Los Angeles to emerge from the pandemic, turn around our economy, create opportunity for all, address homelessness and restore the core services the people of our city deserve,” spokesman Tom Waldman said in an email.

If Biden does select Garcetti for the ambassador post, the City Council would not need to find a replacement immediately. The U.S. Senate would first have to confirm Garcetti’s appointment, a process that could take weeks or months.

The Senate Foreign Relations Committee would take up the nomination before sending it to the full Senate, where a simple majority vote would be needed for approval. However, a single senator can block a confirmation by putting a “hold” on the vote.

“If the person is reasonably competent or a career officer, they will generally go through,” said Ronald Neumann, president of the American Academy of Diplomacy, who has held three ambassador posts.

The confirmation process may be held up if there’s an issue in a nominee’s background or qualifications that poses a problem.

For example, Garcetti could face questions by senators over sexual harassment allegations leveled against one of his former advisers. He could also receive inquiries about the ongoing federal corruption investigation into City Hall, which has resulted in the filing of bribery and racketeering charges against one of his former deputy mayors, Raymond Chan.

Prosecutors have alleged that Chan, while running the Department of Building and Safety, helped then-Councilman Jose Huizar find someone to provide $600,000 to settle a sexual harassment lawsuit filed against Huizar by a former aide. A downtown hotel developer ultimately provided the funds, the indictment said.

An attorney for Chan has repeatedly said his client is innocent and intends to make his case in court.

Times staff writers Noah Bierman, Eli Stokols and Emily Alpert Reyes contributed to this report.