With dozens of seats up for grabs, left-leaning Democrats hope that gains in the City Council could help offset a moderate mayor.In a City Council district in Upper Manhattan, a dozen candidates are on the Democratic ballot, including a former aide to the mayor, a tenants’ rights lawyer, a nonprofit executive, a 21-year-old college student and a drag performer with activist roots.In the Bronx, eight candidates, some of them fresh to politics, are running for a seat left vacant by a longtime political stalwart. And over in Queens, six Democratic contenders are vying for a shot at flipping that borough’s sole Republican Council seat.With New York City voters headed to the polls to pick a new mayor, a contest with significant ramifications for the city’s post-pandemic trajectory, the City Council elections have attracted far less attention. But the city’s legislative body is facing heavy turnover, attracting scores of candidates in crowded races that could prove just as consequential in shaping New York’s future.Left-wing activists and leaders in particular are making an energetic push around Council races, hoping to elect candidates who will advance a progressive platform regardless of the outcome in the mayoral election. The Council votes on the city budget after negotiation with the mayor and plays a key role in the city’s land-use process, which affects development projects.Sochie Nnaemeka, the New York State director of the Working Families Party, said that the City Council can serve “a critical role in either supporting a progressive agenda that the mayor sets out, or blocking and pushing against a restrictive or limited agenda.”All 51 seats on the Council will be on the ballot, and in 32 of those districts the current officeholder will not be running, guaranteeing a plethora of freshman faces. Many incumbents face primary challenges; a handful are new to the job themselves, having won special elections earlier this year. The City Council speaker, Corey Johnson, is among those leaving office, making it unclear who will end up setting the Council’s agenda and negotiating with the mayor.“It’s going to be a dramatic change for everybody,” said Yvette Buckner, a political strategist. In many races, candidates are hoping the electorate sees the possibility of major change as a boon and are seizing the moment.In the Bronx, Rubén Díaz Sr., a Pentecostal minister who created a furor in the Council in 2019 when he said it was “controlled by the homosexual community,” is stepping away from politics after nearly 20 years in public office.Of the eight candidates on the ballot in the district, three — Amanda Farias, Michael Beltzer and William Moore — ran for the seat in 2017. At the time, voters rebuffed their pitches for fresh leadership; this year, that outcome is guaranteed.In District 7 in Upper Manhattan, a group of progressive candidates bonded together, urging residents to wield the ranked-choice voting system to push for real change.Five of the race’s 12 candidates — Marti Allen-Cummings, Dan Cohen, Stacy Lynch, Maria Ordoñez and Corey Ortega — asked voters to rank all of them in the five spots on the ballot. Excluded from the pact was Shaun Abreu, a housing attorney who the current council member endorsed as his replacement.The stakes of the Democratic primaries are especially high in New York, where the winners in nearly every district will be heavily favored to win the general election in November. Only three Republicans serve on the City Council — two from Staten Island and one from Queens.Despite that strong left-leaning base, city voters have tended to be more centrist when choosing a mayor; when Bill de Blasio won in 2013, he was the first Democrat to do so in 24 years. In this year’s election, the more moderate candidates, Eric Adams and Kathryn Garcia, are leading in recent polls.In contrast, progressives have successfully wielded their influence in legislative contests at both the state and national level, including in recent races in which upstarts like Representatives Alexandria Ocasio-Cortez and Jamaal Bowman and State Senator Julia Salazar defeated establishment Democrats by mobilizing left-leaning voters.Ms. Buckner said she expected that same pattern to hold in this year’s elections.“New Yorkers overall are probably going to want a more centrist or moderate voice for mayor, and they’re probably going to go with a more progressive City Council,” she said, “because the issues that are translating on the ground are very different in a smaller community.”The trend appeared to have shaped some progressive groups’ strategies. The city’s chapter of the Democratic Socialists of America has not made an endorsement in the mayor’s race, instead focusing its support on six City Council candidates.In some cases, left-leaning groups are taking advantage of ranked-choice voting to hedge their bets. The Working Families Party, seeing opportunities to pick up seats, began endorsing candidates in City Council races early last fall and has so far backed 30 people in 27 districts.Ms. Ocasio-Cortez, perhaps the most prominent left-wing politician in the state, personally has backed nine candidates in eight Council races. Her political action committee has supported 60 candidates in 31 City Council districts.Ms. Nnaemeka said she believed that the pandemic had voters clamoring for change. Faced with the crisis, many residents have grown more attuned to the impact of local government on their neighborhoods.“We have a tremendous opportunity that came out of crisis to rebuild and reimagine our city,” she said.Gale Brewer, the outgoing Manhattan borough president, is running to reclaim her former City Council seat.Hiroko Masuike/The New York TimesSuch pushes were often felt more closely in the City Council than the mayor’s race, said Bruce Berg, a professor of political science at Fordham University. Over the years, the Council has shifted to the left, he said, in part driven by the city’s changing demographics.“Each of the 51 members is seeking to represent their constituency, as opposed to looking out for the overall interests in the city,” Mr. Berg said.Even so, the makeup of the City Council has not often reflected those demographics, something that many of the candidates are hoping to change.Though more than half of city residents identify as female, only 14 women sit on the City Council. Ms. Buckner, who is leading an initiative to bolster female candidates, said that there were at least six districts that had never been represented by a woman.“There are just so many more candidates running — so many more women, so many people of color in places where you would never have seen them run before,” she said.Ms. Buckner pointed to District 32 in southern Queens, where term limits are preventing the Republican incumbent, Eric Ulrich, from running again. Democrats have targeted his seat, hoping to win the last Republican office in the borough.Queens is one of the nation’s most ethnically diverse counties, and immigrants and people of color have gradually moved into District 32. The pool of Democratic candidates reflects the changing population: Most of the candidates are nonwhite.One reason for the influx of Council candidates, citywide, is the city’s public financing program, beefed up in 2018 to provide an 8-to-1 match to donations of up to $175 from city residents. The system has produced robust fields of candidates for the Council posts. In District 26, which covers parts of Astoria, Long Island City, Sunnyside and Woodside in Queens, 15 candidates will be on the Democratic primary ballot.Many of the dynamics shaping City Council races mirror those shaping the mayor’s race. In several districts, newcomers are squaring off against candidates with political ties.In Central Brooklyn, Crystal Hudson, who has worked for the city’s public advocate and the Council’s Democratic majority leader, is running a tight race against Michael Hollingsworth, an organizer and first-time candidate backed by the Democratic Socialists. Both have endorsements from left-leaning lawmakers — Ms. Hudson was just endorsed by a mayoral candidate, Maya Wiley — and experience has become a major factor in the race.“We need leaders who will hit the ground running and who have a track record of prioritizing those with the greatest needs,” Ms. Hudson said. “I understand the urgency of this moment.”There are also a number of former City Council members looking to return to seats they had vacated and squaring off against newcomers.Gale Brewer, the Manhattan borough president prevented by term limits from running again, is seeking to return to the Upper West Side seat that she left in 2013. Charles Barron, a state assemblyman, is running for his old seat in Brooklyn. It is held by his wife, Inez, who took it from him but faces term limits this year.Regardless of the outcome of the primaries, any referendum on the city’s electoral future that comes out of this year’s Council races could also prove short lived.Because of a provision in the City Charter, the candidates elected this November will only serve a two-year term, instead of the usual four years. After the redistricting process, which takes place every 10 years after a national census, candidates will have to run again along the new district lines in 2023.“Everybody will have to cut their teeth and prove themselves very fast,” Ms. Buckner said. “And then they have to start campaigning again, right after their first year.” More