Clement was eight years old when his father, Frank G. Clement, was first elected governor of Tennessee. He became enamored of politics at a very early age, and was widely regarded as quite an asset in his father's subsequent gubernatorial campaigns in 1954 and 1962, receiving the nickname "Little Bob", which has never fully left him (he is approximately 5'5"/165 cm tall).

Clement attended the prominent Hillsboro High school in located in the Green Hills neighborhood of Nashville. He went on to attend the University of Tennessee, graduating in 1967, He served in the National Guard from 1969 to 1971; he served in the reserves until 2001, retiring as a colonel.

Clement considered buying a telephone company while still at UT, but his father refused to lend him the money. However, he did learn quite a bit about the Tennessee Public Service Commission, which regulated phone companies and other utilities. He wanted to get a job on the commission's staff, but chairman Hammond Fowler kept blowing off his requests. When Fowler, who held the East Tennessee seat on the commission, ran for a fourth six-year term in 1972, Clement ran against him in the Democratic primary. Bolstered in part by a televised debate in which he appeared to be young and vibrant while Fowler appeared to be old and doddering, Clement won by an incredible 3-1 margin--the most lopsided defeat of a statewide incumbent in Tennessee history. He overwhelmed Republican nominee Tom Garland in the general election what was otherwise largely a very good year for Republicans in Tennessee (and nationwide) running for major offices. (No Republican was ever elected to the Public Service Commission in Tennessee during its existence, which later played a factor in its abolition more than 20 years later.) At 32, he was (and still is) the youngest person ever elected to statewide office in Tennessee history.

In 1978, Clement announced he would run for the Democratic nomination for governor. He ran second in the primary behind Knoxville banker Jake Butcher, who had finished second in the Democratic gubernatorial primary four years previously and who had a level of name recognition roughly equal to Clement and, additionally, greater financial resources. (Butcher's total expenditures in running for governor of Tennessee that year exceeded $4,000,000, a then unheard-of amount for a relatively small state. By comparison, Jerry Brown in the same year also spent about $4,000,000 running for re-election as governor of California, a far larger state in both area and population. Butcher nonetheless lost the general election to Republican Lamar Alexander.)

Clement was not unemployed for long. In 1979, President Jimmy Carter tapped him for an unexpired term on the Board of Directors of the Tennessee Valley Authority. Clement made this office a high-profile position (at this time, the TVA Board had only three members and unlike most similar positions was a full-time job), largely as an opponent of then-TVA Chairman S. David Freeman, who was seen by many (including most TVA employees) as both too environmentalist and insufficiently pro-nuclear.

In 1982, Clement announced his candidacy for the 7th Congressional District, his family's home district. The seat was being vacated by five-term incumbent Republican Robin Beard, who was leaving it to run against Senator Jim Sasser, and had been renumbered from the 6th in redistircting. Clement defeated Bartlett banker Harold Byrd for the Democratic nomination for Beard's former seat but was narrowly defeated in the general election by Don Sundquist, a businessman from Memphis who would later become a two-term governor. It was the first (and as of the 2004 elections, only) time that a Democrat had come within single digits in the 7th District since it fell into Republican hands in 1972. Clement said years later that he'd made a mistake by trying to run the same kind of campaign that his father had in his glory days.

Temporarily out of politics, Clement remained active in Democratic circles. He also had a large network of contacts through his ongoing service in the National Guard. In 1983, Clement became president of Cumberland College, a struggling private junior college 30 miles east of Nashville in Lebanon, Tennessee. This institution, founded in the 1840s, had at one time been a prestigious university but had fallen upon hard times, never fully recovering from the Great Depression and the widespread availablity of lower-cost public higher education after World War II. The low point in its problems probably occurred in the early 1960s when it was forced, for financial reasons, to sell its once-renowned law school (which Clement's father had attended) to what is now Samford University. During Clement's tenure, the school reobtained four-year college, and shortly later, full university status, and today Cumberland University is considered still to be on a sound financial footing, largely as a result of Clement's tenure as president.

In 1987, 5th District Congressman Bill Boner left his House seat to become mayor of Nashville. Clement, who had moved to Nashville by this time, resigned as president of Cumberland on August 22 to run in the Democratic primary for the balance of Boner's term. He won the nomination over a crowded field, including most prominently Phil Bredesen, future mayor of Nashville and current governor of Tennessee, who finished second. As the Republicans had long since lost interest in a seat they hadn't won since 1875 (Democrats have faced only token opposition since 1972), Clement's victory in the special election of January 19, 1988 was a foregone conclusion. He took office that night, as soon as the results were certified. He was unopposed for a full term in November and was reelected six times against almost no opposition. Clement established himself as one of the leading moderates in the Democratic caucus, and was a cofounder of the Blue Dog Coalition.

In 2002, when Republican Senator Fred Thompson stated that he had changed his mind regarding his previous announcement that he would run for a sedond full term, Clement entered the Democratic primaryfor Thompson's seat. He won the nomination fairly easily, but was soundly defeated (by a margin of almost 10 percent) in the November general election by former governor Lamar Alexander. Clement remains active in Democratic political circles and University of Tennessee alumni activities. His name has recently surfaced as a possible successor to current Nashville mayor Bill Purcell in 2007, and he was also discussed as a potential contestant for the Senate seat currently held by Senate Majority Leader Bill Frist, who is not seeking a third term. However, it was announced on February 15, 2006, that Clement was forming an exploratory committee to raise funds for a potential race for mayor of Nashville.

Clement is a Southern Baptist, but attends Christ Church, a large charismatic church in Nashville.