Bedfordshire-born Paul Peterson joined United straight from school in 1966 and signed professional terms in December 1969.

A left-back, he spent most of his time at Elland Road in the reserves. His first-team debut came on Easter Monday 1970 when manager Don Revie fielded a team made up entirely of second string players in order to protect his regulars. Leeds had been competing for three trophies, but fixture congestion had left the players exhausted and Revie chose to surrender the league to Everton. The 30 March match was at the Baseball Ground against Derby County and Leeds lined up thus: Harvey, Davey, Peterson, Lumsden, Kennedy, Yorath, Galvin, Bates, Belfitt, Hibbitt, Johanneson. The Whites were beaten 4-1.

Peterson played again five days later against Burnley at Elland Road. United defeated the Turf Moor outfit 2-1 with a memorable brace of goals from Eddie Gray. Richard Ulyatt in the Yorkshire Post remarked that 'Peterson [looked] as though he had taken his cue from Cooper.' High praise, indeed!

Peterson came off the bench as a replacement for John Faulkner when the latter fractured a knee cap against Manchester City on 18 April.

He made his final first team appearance three days later in a 3-2 defeat at Ipswich. Of the selection that day only Gray and Peter Lorimer were recognised first-teamers. Peterson came close to preventing Jimmy Robertson scoring the third Ipswich goal; he tried to block the shot on the line, but only succeeded in helping it into the net.

The following September the young defender was included in the United squad to play Sarpsborg at Elland Road in the Fairs Cup when a number of regulars were unavailable through injury. However, he did no more than keep the bench warm as Leeds won by five clear goals.

Knowing senior opportunities would be scarce at United, Peterson chose to make a new start at Second Division Swindon Town in June 1971, moving to the County Ground on a free transfer. He couldn't make a breakthrough and his only senior appearance came in January 1972 when the Robins lost 4-1 at Birmingham City.

Peterson went into non-league football shortly afterwards, joining Stevenage Borough; he later served the club as coach and assistant manager.