Kaywin Feldman crossed the still sunny atrium of the East Building of the National Gallery of Art a little after 6 p.m., while a line of guests waiting to get into the gallery’s “Evenings at the Edge” program snaked down the street and around the corner.

In her fourth day as the museum’s fifth — and first female — director, Feldman was met by communications chief Anabeth Guthrie, who gushed about the more than 9,000 people registered for the event, featuring a female tap group, pop-up gallery talks and cash bars.

Guthrie and chief of security Mark Wallace had wagered a cup of coffee on the night’s final attendance, with Guthrie guessing 4,000 and Wallace 5,000.

“Can I get in on it?” Feldman asked about the wager. She estimated 5,200.

The exchange highlighted both Feldman’s optimism and enthusiasm, traits that should prove useful as she takes control of the national art museum. She started the job March 11, and her schedule was crammed with meetings and receptions to introduce her to the staff and the Washington arts community.

The federally supported museum is renowned for its collection of masterworks, including pieces by Rembrandt, Monet, Picasso and Pollock, and it attracts about 5 million visitors annually to its two buildings and sculpture garden. But the gallery faces serious challenges. Some — such as how to attract modern audiences and engage with issues they care about — are affecting museums across the country. Other challenges are unique to the quasi-federal institution, including a staff hindered by low morale, charges of sexual harassment and retaliation, and high turnover among gallery guards. The museum began contracting with a private security firm late last year because it didn’t have enough personnel to keep all of its galleries open.

Feldman’s experience, at museums in California, Tennessee and most recently, the Minneapolis Institute of Art, as well as her leadership of national museum organizations, attracted the board of trustees, gallery president Frederick W. Beinecke told about 70 guests at an afternoon tea last week. “She not only has led museums, but she has led managers of museums,” he said.

Feldman, 52, told the guests she has a lot to learn.

“I want to get to know the staff. I want to get to know the institution’s values. . . . I want to get to know the collection,” she said.

She got a head start on all three during her whirlwind first week. Feldman and her husband, Jim Lutz, spent the Saturday before her first day observing the education department’s family workshops, attending a lecture by artist Alex Katz in conversation with modern art curator Harry Cooper and, of course, wandering the galleries.

Feldman held a gallery-wide staff meeting on her first day, and on her second, she attended the guards’ morning roll call, greeting the officers individually. She also spent a full day that week attending new-employee training, which she could have skipped.

“It’s good to have a one-day deep dive, to experience what all new employees experience,” Feldman said of the session. Her main takeaway? “The commitment to excellence, at every department, at every level. And the warmth and enthusiasm of the presenters. They love this place.”

Mel Harper, a member of the education department, noted Feldman’s positivity and humor.

“She’s very funny, and she said she wanted to meet us all. That really stuck with me,” said Harper, who wore a handmade button that read #Kaywinning.

There were also receptions for the media, local cultural leaders and donors, as well as events marking the much-anticipated Tintoretto exhibition. In remarks to each group, Feldman emphasized the honor and privilege of leading the museum, and she spotlighted the staff, leading applause for them and their “standard of excellence.”

Feldman repeatedly thanked her predecessors, and especially Earl “Rusty” Powell III, who retired this month after 26 years as director. Powell, like J. Carter Brown before him, has been given the title director emeritus, which comes with a salary, an off-site office and a part-time assistant for two years. Powell and Carol Kelley, who retired this month from her position as the gallery’s chief of protocol and special events, will be paid with private funds.

“I am delighted that Rusty’s exemplary service has been recognized with an emeritus status,” Feldman said. “Rusty is a tremendous resource for both me and the board of trustees, and I look forward to taking advantage of his years of experience and insight.”

At the after-hours event — which attracted about 3,300 people, setting a record for the series even as it fell short of the wager — Feldman snapped photos, asked questions of staffers giving presentations on abstract expressionism and greeted guests who were making female superhero collages. A few recognized Feldman as the new director, including Tom Gilday of Chevy Chase, a docent for 30 years who introduced her to his wife and three daughters.

After the exchange, Gilday said that the museum is “ready for some fresh ideas” but that he expects change to come slowly.

“This is not a job where someone is looking over your shoulder. This is a long-term position,” he said. “I don’t think in six months or eight months anyone on the board is going to say, ‘What’s up?’ ”