The Children’s Museum of Manhattan had planned to announce the appointment of Aileen Hefferren as its new chief executive and director on Tuesday. But the board decided to wait till Wednesday in deference to Blackout Tuesday, a social media action intended to show solidarity with the protests over the death of George Floyd.

The Children’s Museum is among a growing number of arts institutions from New York to Virginia to Colorado trying to navigate the sensitive, uncharted territory of making major appointments and initiating new cultural leaders in this difficult cultural moment.

And new appointees find themselves stepping into positions of leadership made much more complicated by questions such as when and how to safely reopen, how to stem financial losses caused by the pandemic and how to respond to a country convulsed by unrest.

Often, the announcements have been drowned out by the drumbeat of news that has accompanied the coronavirus outbreak — namely layoffs and furloughs — and by the more recent demonstrations in scores of American cities.

“They’re looking for people who are tested, with a level of competence and confidence that will inspire them to feel comfortable, as well as give the staff comfort that this person understands what they’re up against,” said Sarah James, who specializes in cultural executive searches at the firm Phillips Oppenheim. “Nobody really knows how to deal with this.”

Since Ms. Hefferren doesn’t take the position until Sept. 15, the Children’s Museum might have waited even longer, but it was eager to get things moving, in light of pressing matters like seeking public approval for its new home in a former church on Central Park West; the need to reconceive its interactive exhibitions with coronavirus considerations in mind; and the economic losses resulting from months of lockdown.

“We certainly expect her to lead and take charge of reimagining what our institution can and should be,” said Matt Messinger, a co-chairman of the museum’s board.

Over the last three months, Timothy R. Rodgers became the new director of the Phoenix Art Museum; Kathleen Bartels was named the next executive director of the Museum of Contemporary Art in Toronto and Nicola Lees was appointed head of the Aspen Art Museum.

Other new hires include Jaynelle Hazard, director at the Greater Reston Arts Center in Reston, Va.; Amanda Lahikainen at the Ogunquit Museum of American Art in Maine; and Matthew Clarke at the Design Trust for Public Space in Manhattan. Becca Hoffman is the new managing director of three art fairs — in Aspen, Chicago and Palm Springs.

“It’s a very unique time to accept a new role,” Ms. Hoffman said. “It’s been a challenge.”

While institutions might be expected to suspend hiring, some have accelerated or even initiated searches, given the current need for strong leadership. But candidates want to make sure that the boards doing the hiring aren’t looking for business as usual. “They don’t want to just come in and stabilize, because nobody believes in going back,” Ms. James said of candidates. “Everybody believes you’re going to die as an institution or you’re going to go forward as something better.”

Executives’ job descriptions are changing under their feet, requiring skills in handling not only a global health crisis but also issues of racial equity. Ms. Hefferren’s background would seem to make her well-equipped to lead the Children’s Museum, given that she comes from Prep for Prep, the nonprofit organization that offers promising New York City students of color access to a private school education.

She said she hopes to bring that experience to her new position, expanding the museum’s outreach to families in homeless shelters, for example, affordable housing residents and incarcerated parents. “It’s definitely a challenging time for our country and for New York,” Ms. Hefferren said. “But it also just makes the need for the Children’s Museum that much more apparent.”

The museum, on West 83rd Street in Manhattan, continues to move forward with its ambitious renovation of a former church that it bought for $45 million on Central Park West at 96th Street, which goes before the Landmarks Preservation Commission next month. Because its typically hands-on installations have yet to be designed, the museum will be able to make adjustments in light of social-distancing considerations.

Ms. Hoffman, the former director of the Outsider Art Fair — who now oversees Intersect Aspen (formerly Art Aspen); Sculpture Objects Functional Art and Design Chicago; and Art Palm Springs — has started her position at a time when the future of art fairs seems to hang in the balance with the current bans on large gatherings.

Many in the art market predict that the proliferation of art fairs over the last few years will shake out, leaving only the strongest standing, and that the pivot to online formats may force galleries to reassess whether the steep cost associated with a fair (including travel, shipping and insurance) is worth it.

But Ms. Hoffman remains optimistic. “I don’t think that they will ever go away,” she said. “But I believe there will be more of a regional focus moving forward and you will need to have a proper digital presentation. You need to have the connectivity for people who aren’t going to recover from this as quickly as others.”

The obstacles, she said, include trying to network in places like Aspen — where her first (now virtual) fair is coming up on July 22 — without being able to meet face-to-face. “It’s kind of like, ‘Please introduce me to this person, please introduce me to that person,’” Ms. Hoffman said. “It’s a big hurdle to ingratiate yourself in a community when it’s on the phone or on Zoom.”

Ms. Hazard was selected to run the Greater Reston Arts Center in Virginia just as the pandemic was descending. “The interview process was completely on Zoom — I still haven’t met my staff or my board of directors,” she said. “I’m focusing on what I have control over — my mind, my schedule, my well-being — rather than what I don’t have control over: the virus, the justice system.”

She has instead taken proactive steps such as bringing the museum’s exhibitions online and rewriting its diversity statement. “We have to constantly think about how to impact our communities and stand behind them,” Ms. Hazard said, “to confront hate, to use compassion, to use empathy.”

Mr. Rodgers in Phoenix has been thinking about how to be helpful to local galleries that are struggling — perhaps displaying (without selling) their artists’ work on the walls of the museum’s restaurant. “The museum exists within a larger community and ecology of art,” he said. “How is it that we can sustain and grow back what it is that we’re losing during this?”

To be sure, the moment has also been challenging personally. Ms. Bartels had to start her Toronto job while living in an Airbnb and has yet to be able to look for permanent housing. And none of these promotions is getting the usual laudatory attention. But appointees say acknowledgment is an afterthought; there is too much work to be done. “It’s a chance to be a leader and to lead on an issue we all care about — the importance of public space,” said Mr. Clarke of the Design Trust. “We need to lean into that.”

Above all, newly appointed cultural leaders say, they realize that the world has limited bandwidth right now, not to mention more urgent concerns.

“At the end of the day, I want everybody to be safe,” Ms. Hoffman said. “I don’t need to do my own celebration. I just want us to get to a place where we can all come out and actually feel comfortable seeing one another.”

The Trump administration on Wednesday said it planned to block Chinese airlines from flying into or out of the United States starting on June 16, after the Chinese government effectively prevented U.S. airlines from resuming service between the countries.

The dispute stems from a March 26 decision by China’s aviation regulators that limited foreign carriers to one flight per week based on the flight schedules they had in place earlier that month. But all three American airlines that fly between China and the United States had stopped service to the country by then because of the coronavirus pandemic. As a result, the Chinese government had effectively banned them from flying there at all, even though airlines from that country continue to fly to American cities.

As ground zero of the pandemic, China was the first country to see aviation grind to a halt this year. In January, American and Chinese carriers operated about 325 weekly flights between the two countries. By mid-Feburary, only 20 remained, all of them run by Chinese airlines.

The March decision became a problem only in recent weeks, as Delta Air Lines and United Airlines had hoped to resume flights to China starting this month. Both carriers appealed to the Civil Aviation Authority of China, but did not receive a response. The U.S. also pressed Chinese officials to change their position during a call on May 14, arguing that the country was in violation of a 1980 agreement that governs flights between the two countries and aims to ensure that rules “equally apply to all domestic and foreign carriers” in both countries.

China’s aviation authority told American officials that it was considering amending its rule, but it has not said “definitively” when that might happen, the Transportation Department said in a statement. “In light of these facts, which present a situation in which the Chinese aviation authorities have authorized no U.S. carrier scheduled passenger operations between the United States and China, we conclude that these circumstances require the department’s action to restore a competitive balance.”

Tensions between the United States and China have escalated sharply in recent weeks as the countries scuffle over the origin of the pandemic and China’s recent move to tighten its authority over Hong Kong, a semiautonomous city. With the presidential election just five months away, President Trump and his campaign have taken a much tougher stand against China, blaming its government for allowing coronavirus to turn into a pandemic and wreck the American economy.

In mid-May, the Trump administration expanded restrictions on Huawei, the Chinese telecom firm, and blocked a government pension fund from investing in China. Last Friday, Mr. Trump announced that he was beginning the process of ending the American government’s special relationship with Hong Kong, and that his administration would place sanctions on officials responsible for Beijing’s rollback of liberties in the territory.

“The Chinese government has continually violated its promises to us and so many other nations,” the president said at the time. “The world is now suffering as a result of the malfeasance of the Chinese government.”

Ana Swanson contributed reporting.