Glover was born and attended public schools in Jacksonville. As a young man he experienced the racism of the early 1960s when he stumbled into Ax Handle Saturday. On that day, a group of 200 middle-aged and elderly white men, including some members of the Ku Klux Klan, gathered in Hemming Park, armed with axe handles and baseball bats, and attacked Civil rights protesters. A group of black youth who were called the "Boomerangs" attempted to protect the demonstrators. Police, who had not intervened when the protesters were attacked, now became involved, arresting members of the Boomerangs and other black residents who had attempted to stop the beatings. Glover said he ran to the police, expecting them to arrest the thugs, but was told to leave town or risk being killed. Glover graduated from Edward Waters College in 1966 and received a master's degree from the University of North Florida; he also graduated from the 130th Session of the FBI National Academy. Glover was a starting linebacker and team captain for the Edward Waters College football team, where he was a teammate of Jim "Cannonball" Butler.
Glover joined the Jacksonville Sheriff's Office in 1966, becoming an investigator in the Detective Division in 1969 and was promoted to Sergeant in 1974. In 1991, he was named Director of Police Services, one of the JSO's top positions. A political Democrat and a long-time police officer, Glover was elected Sheriff of Jacksonville in 1995, and was re-elected in 1999. Glover was serving at the time of the Brenton Butler case in 2000, in which the 15-year-old Butler was falsely accused of murder. Butler confessed to the crime, but later testified that two JSO detectives, including Nat Glover's son Michael Glover, had physically attacked and coerced him into confessing. Butler was acquitted and the JSO and State Attorney's Office took the unusual step of apologizing to him. Michael Glover, who denied the allegation, retired from the Sheriff's Office to become a private investigator.
Mayoral candidate and later life
In 2003, Nat Glover ran for Mayor of Jacksonville but was defeated by Republican candidate John Peyton, in the most expensive mayoral race in Jacksonville's history. An African-American had never served as mayor in Jacksonville, until Alvin Brown's election on May 19, 2011. Glover's campaign focused on education, economic development, and managing the city's growth. "Jacksonville is poised for greatness. I want to be the mayor that allows us to show the state how great we are", Nat Glover said. The campaign was briefly marred by racism; after Matt Carlucci, a white Republican candidate, endorsed Glover after being defeated in the open primary, his business was vandalized with racial slurs against Glover. Vandals also spray-painted racist graffiti on Glover's headquarters, though witnesses to the crime described the vandals of this incident as being black males. After retiring from the Jacksonville Sheriff's Office Glover served on several boards, and was hired as a special adviser by University of North Florida President John Delaney, the former Mayor of Jacksonville. Glover and his wife Doris J. Bailey have two children, two grandsons and a granddaughter. He says his most admired people are Martin Luther King, Jr. and the Wright brothers. Nat Glover stated "I always felt like if I could make the children and the senior citizens safe, everyone in between would be OK".
Edward Waters College
During his career, Glover maintained a relationship with his alma mater, where he is a member of Omega Psi Phi fraternity. In 2005, he served on Edward Waters College's presidential search committee, which was formed after a plagiarism scandal led to accreditation problems and the resignation of President Jenkins. That committee took two years to select Claudette Williams in 2007. Glover joined EWC's Board of Trustees in 2008, and when Williams resigned effective May 15, 2010, Glover was quickly approved as interim president. In February 2011, the position was made permanent. In the summer of 2014, Glover was a finalist for the HBCU Digest male president of the year. In , Glover recounted his journey to become president of his alma mater. In September 2017, Glover announced that he will be retiring in May 2018.