From Wikipedia,

The police abolition movement is a political movement, largely in the United States, that advocates replacing policing with other systems of public safety. Police abolitionists believe that policing, as a system, is inherently flawed and cannot be reformed—a view that rejects the ideology of police reformists. While reformists seek to address the ways in which policing occurs, abolitionists seek to transform policing altogether through a process of disbanding, disempowering, and disarming the police. Abolitionists argue that the institution of policing is deeply rooted in a history of white supremacy and settler colonialism, and that it is inseparable from a pre-existing racial capitalist order.

In the summer of 2020, a movement to dismantle the Minneapolis police department became supported by a majority of the members of the Minneapolis city council, but was later abandoned.

Some have questioned the practicality of police abolition, asking whether it would be possible to maintain a society with no police without it devolving into lawlessness and chaos. As one potential response, the capitalist philosopher Michael Huemer has written at length about how a society that abolished government policing could maintain the public order. From his book The Problem of Political Authority,

According to a recent report, there are now 20 million private security guards worldwide – about twice as many as the number of government police. In America, private security guards number about 1 million, compared to 700,000 government police. In some cases, the government itself hires private security guards to protect public spaces, including the Liberty Bell in Philadelphia, the Statue of Liberty in New York, and the main bus terminal in Durham, North Carolina. If this trend continues, we could one day see a situation in which all public spaces are protected by private security guards.

In many countries – the United States, the United Kingdom, Canada, Australia, and others – private citizens are legally authorized to make citizens’ arrests. The conditions for a legal citizen’s arrest, however, tend to be much more restricted than the conditions under which government police may make an arrest. Legal authorization for citizens’ arrests may be limited to certain kinds of crimes, and the arresting citizen may be required to personally witness the crime in progress. One could imagine a liberalization of such laws, permitting citizens’ arrests for all crimes, including cases in which the suspect’s guilt is established by investigation after the fact.

Will a large American city fully abolish their police department before 2035?

This question resolves positively in the event that an American city whose metropolitan area contains at least 1 million people, abolishes their public police department. In other words, the government would need to take an official action whose result is the complete disappearance of a taxpayer funded and government managed police department in that city.