Moncur made his full league debut as an 18-year-old in a Division Two clash between Newcastle and Luton in 1963. However, he proved to be something of a slow developer and was nearly sold to Norwich for as little as £25,000. This deal fell through and made Bobby more determined than ever to improve his game, Helping Newcastle to promotion as Division 2 champions in 1965. In 1971, his revival complete in some style, manager Joe Harvey described him as "the supreme sweeper and a most valuable asset both to Newcastle United and Scotland".
Bobby played a total of 296 times in the famous black and white shirt, scoring three goals - all in the two-legged final of the 1969 Fairs Cup. He also played 16 times for Scotland between his debut in 1968, against the Netherlands, and 1972. In 1974 after Captaining Newcastle in the FA Cup final, he was transferred to Sunderland, moving again to Carlisle United in 1976, where he ended his playing career.
Bobby Moncur captained the Newcastle United team that won the 1969 Inter-Cities Fairs Cup Final, against Ujpesti Dozsa. Over the two legs he scored two goals in the first game and one more in the second leg, with Newcastle running out 6 - 2 winners.
Nowadays, Bobby makes semi-frequent appearances on Sky TV as a football pundit. He currently holds the record of being the last Newcastle United captain to lift silverware with the club, and is frequently quoted as wanting to lose this honour as quickly as possible.
Moncur lives in the Low Fell area of Gateshead and is married to Camille and together they have two children, Paul and Angela. He is regularly seen enjoying swimming and steam room sessions at the Durham CCC Bannatyne gym. In September 2007, Moncur was diagnosed with cancer of the colon, but nine months later he was told he was cancer free.