With his historic pick of Keechant Sewell, Mayor-elect Eric Adams made good on his vow to select a woman as the city’s 45th police commissioner. While she faces a steep challenge running so large a department, all signs are promising.

The Queens-born, 20-year police veteran is saying all the right things, and Adams’ other top choices have impressed: He’s so far earned the benefit of any doubt.

Most important, she’ll have the mayor’s full backing in moving to crack down on crime and disorder, without the crippling appease-the-most-radical-critics approach of the de Blasio era.

Dermot O’Shea and James O’Neill served honorably, but City Hall interference hamstrung them time and again. Nor is Sewell’s resume that light: She’s an FBI-trained hostage negotiator, with service undercover and on the New York-New Jersey Joint-Terrorism Task Force, as well as the Nassau County Police Department’s chief of detectives.

“Violent crime is the No. 1 priority,” Sewell told reporters Wednesday, vowing to be “laser-focused” on gun crime and taking violent criminals off the streets. And she’s plainly onboard with Adams’ vow to restore anti-crime units. Crucially, she proudly embraces “broken windows” policing, the anti-crime strategy key to the NYPD’s historic victories of recent decades.

Griping about the brass is a time-honored tradition, but every member of the department has to feel great relief that the chain of command will again have their backs as they work to keep New York safe.