In 2023, Adrienne Adams, the City Council speaker, rejected a call from the body’s most progressive members to reduce the size of the Police Department.

A year later, Ms. Adams led a rare override of a mayoral veto to push through the How Many Stops Act, a police accountability bill that requires police to record the race, age and gender of most people they stop.

Those decisions — one responding to the concerns of the department, the other to New Yorkers worried about police overreach — reflected a common-sense approach to policing that Ms. Adams says distinguishes her from her opponents in the June 24 Democratic primary for mayor.

Ms. Adams sought to build on that image on Thursday, releasing a detailed plan to address public safety, in which she vowed to fill the more than 2,400 vacancies in the Police Department in her first eight months in office.

She plans to offer housing and tuition support to attract new officers and modernize CompStat, the Police Department’s crime data system, to track officer recruitment, retention and trust levels between the police and community.

She said she would also move to increase the number of officers in the subway and have them focus on crime prevention while having mental health professionals and social workers deal more with homeless and mentally ill people.