Robert F. Larke was the only child of parents who lived in Greenpoint, Brooklyn. He served four years in the United States Navy during the Vietnam War and, after his honorable discharge, returned to New York City and worked as a teller at Greenpoint Savings Bank. After seeing a flyer for the police examination while visiting friends in Queens, he took the test and joined the New York City Police Department on 3 April 1968, at the age of 24.
The next day Martin Luther King, Jr. was assassinated, and recruits from the Police Academy were sent onto the streets in their gray uniforms. After the assassination of Robert Kennedy that June, the recruits stayed on patrol for the rest of their training. Officer Larke was later assigned to a highway car in a motorcycle unit and then to the 19th Precinct on the Upper East Side. While studying at night at the New York Institute of Technology and John Jay College of Criminal Justice, he took a day position as a criminal analyst. When budget cuts removed uniformed members from that post, he moved to the Central Personnel Index, where he was promoted to detective on 24 May 1988 and to second grade on 27 June 1997. He earned a bachelor's degree in criminal justice from the New York Institute of Technology in Old Westbury.
Detective Larke reached the mandatory retirement age and retired from the Central Personnel Index unit of the Employee Management Division on 30 November 2006, after 38 years with the department. He was known as a quiet, steady and dependable worker. He had spent many hours in the field during the rescue and recovery after the World Trade Center attacks of 2001, and the illnesses he developed in retirement were linked to that work. He died on 7 June 2017, at the age of 73 and a half, and his death was ruled in the line of duty.
He was survived by his wife and three sons. His name was added to the NYPD memorial wall at Battery Park City on 11 October 2019, and in 2019 also to the police memorial walls in Albany, New York, and Washington, D.C.