Staunch Critic of the N.Y.P.D. Grapples With Deaths of 2 Officers

Ms. Jordan, too, has deep roots in the area, describing herself as a third-generation Harlemite. She attended the Calhoun School, a progressive private school on the Upper West Side, and Brown University and built a career around activism — she was involved in the Black Lives Matter and Occupy Wall Street movements and founded a “cop watch” team, she has said. And she spent time writing and in publishing, including releasing a book that grapples with her personal experiences with domestic violence.

She ran for City Council last year, initially inspired, she told The Nation, by the left-wing members of the “Squad” in Congress. Ms. Jordan identifies as a Black socialist, though groups like the Democratic Socialists of America and the left-wing Working Families Party made no endorsement in her primary.

Other prominent left-wing organizations, including the political group associated with Representative Alexandria Ocasio-Cortez, did offer support, though to date Ms. Jordan is not considered a prominent member of the city’s left wing — she is largely unknown even to like-minded officials.

In the ranked-choice primary election, she ultimately prevailed over the incumbent by around 100 votes.

Asked to assess her performance so far in office, Keith L.T. Wright, the chairman of the Manhattan Democratic Party, replied, “I’ve never had a conversation with her, and I don’t know what she does.”

(Ms. Jordan said she welcomed conversations and noted her relationship with the Manhattan Young Democrats. “The future of the Democratic Party is progressive and bold,” she said.)

Patrick J. Lynch, the head of the Police Benevolent Association — a union considered toxic by many Democrats for, among other things, endorsing Donald J. Trump in 2020 — also said that Ms. Jordan “is new to the office and we have had no interactions with her.”