In May, Ms. Allen replaced the longtime cartoon editor, Robert Mankoff, who has moved to Esquire, where he is its new humor editor. Mr. Mankoff was the star of a 2015 documentary, “Very Semi-Serious,” that showcased the magazine’s process of sifting through 1,000 cartoons every week to settle on the 15 or so that make it into print. Every Tuesday, artists still come into the office to pitch their cartoons directly to the cartoon editor.

With an easy, self-deprecating laugh, Ms. Allen described her first exposure to running this system. (When editors at The New Yorker turn down a pitch for an article, they rarely do it face to face.) “It took me the first 10 people being, ‘I’m so sorry, I’m so nervous,’ and they were like, ‘I’m so sorry, I’m so nervous,’” she said, with two weeks under her belt. “They were like: ‘We’re trying to sell you work.’ And I was like: ‘I’m trying to sell myself.’ I’ve been buying them pastries, literally buttering them up.”

Ms. Allen has a sprawling set of responsibilities: She also edits the daily cartoons for The New Yorker online; works on video and radio humor pieces for the magazine; runs its humor Twitter account; and for three years has edited Daily Shouts, comic essays that have become one of the most popular features on the site. (According to the magazine, in the past three months, traffic to those essays is up 60 percent from last year.)

Her ability to find new voices for Daily Shouts is what first drew the attention of The New Yorker’s editor, David Remnick. “She was bringing in people and things that I hadn’t heard before, and sometimes you need to reinvigorate parts of the magazine,” he said by phone, adding, “We need to have a deeper exploration of the web, as far as cartooning.”

Ms. Allen, who grew up on the Upper West Side, has in some ways been preparing for this job her whole life. As a child, she cut out The New Yorker cartoons and filed them with “an archival drive” matched only, she said, by her collection of photos of Leonardo DiCaprio. She attended Brearley School in Manhattan, where, she joked, her comic career was born. “I went to an all-girls school for 13 years whose mascot is the beaver,” she said. “You cannot come out at the other end of that without a sense of humor.”