Six foot tall North Easterner David Kennedy joined Leeds United as an apprentice and signed professional forms for the club in May 1968.

Nicknamed Jack by the other players after the US President, the central defender scored on his first-team debut at Derby County in March 1970. Don Revie's eleven for the game consisted entirely of reserves because of the fixture congestion facing his treble-chasing team. The youngster struggled to contain an in form Rams forward line and United lost 4-1, but, according to Barry Foster of the Yorkshire Post, 'Kennedy and Yorath were the pillars of the Leeds defence.' Kennedy was responsible for United's consolation goal, which the Evening Post's Phil Brown described as 'a Charlton-like header' from Mick Bates' corner kick.

The novice defender made two further appearances for the first-team, both in 1970. In the 3-2 league defeat at Ipswich on 21 April he cleared one effort off the line. When Leeds faced Sarpsborg in a UEFA Cup-tie in Norway on 15 September, Revie turned to Kennedy with Jack Charlton, Terry Yorath and Paul Reaney injured and Norman Hunter being rested. As per Barry Foster, 'Leeds' goal was never in real danger and Sprake was more or less a spectator for much of the game. Kennedy also had little to do and for much of the time the defence was made up of the 19-year-old reserve centre-half with the aid of either Madeley or Cooper.' Leeds were not at their best but won with a goal from Peter Lorimer.

Kennedy was on the bench in the return leg in West Yorkshire and was also non-playing sub when Leeds beat Derby at the Baseball Ground in October 1970.

He may have harboured dreams of being the long-erm replacement for Charlton, but the signing of John Faulkner from Sutton United in 1970 sent him down the pecking order, and when Faulkner recovered from a kneecap injury , Kennedy departed Elland Road on a free transfer to Fourth Division Lincoln City in July 1971. He scored on his Imps debut, on 1 September in their 3-1 defeat at Crewe. Kennedy made 6 league appearances for City plus 2 more from the bench that season, but struggled to make any sort of impact. His final appearance came in a Watney Cup-tie at the end of July 1972 against Burnley.

Kennedy drifted out of the senior game after leaving Sincil Bank in September 1972.