Born in Leith on 31st Januay 1925 Paddy started his career with Bo'ness United before turning senior with St Johnstone in 1948. At Muirton Park Paddy quickly developed into a top rate senior goal scorer and in April 1952 the Dons moved in with a £7,500 bid to bring Paddy to Pittodrie. Buckley's electrifying pace was superbly supported by the quickness of Jackie Hather on the left wing and eventually by the class of Graham Leggat on the right flank. Harry Yorston and at first Gorge Hamilton, then latterly Bobby Wishart provided Paddy's principal inside forward support.

Buckley's arrival marked a general upsurge in the Dons fortunes in the early 1950s and his role in transforming Aberdeen from perennial bridesmaids into Scottish Champions in 1955 was not insignificant. Paddy's first full season at Pittodrie brought him a modest haul of 15 goals in domestic competition but the following season, 1953-54, saw him fulfil his true potential as he hit the net on no less than 27 occasions in 38 League and Cup outings. The Dons reached the final of the Scottish Cup in 1954 with Buckley scoring in every round, bar one, on the Dons march to Hampden. In the final against Celtic Paddy scored a superb equaliser for the Dons but alas Celtic prevailed 2-1.

However, Paddy's scoring exploits had caught the eye of the Scottish selectors and he was called up for the game against Norway at Hampden on May 5th 1954. He didn't travel to Switzerland for the World Cup but Paddy was recalled for the first post World Cup game against Wales in Cardiff. Paddy didn't let the side down he scored the only goal of the game and three weeks later he was selected for the Home International against Northern Ireland. That game against Wales proved to be Paddy's last for Scotland as Hibs Lawrie Reilly made the Scotland No.9 jersey his own for almost three years.

At Pittodrie Paddy continued to bang in the goals and thrill the crowds with his lightning pace and his amazing jumping ability. His 17 League goals were a major factor in the Dons 1955 Championship triumph, none more so than his hat-trick in a crucial 4-0 win over Rangers that all but clinched the title. In November 1955 he picked up a serious knee injury from which he never fully recovered. Paddy's Pittodrie career ended prematurely in 1957. Buckley's three internationals saw him score one goal and it was probably no accident that on that occasion in Cardiff Paddy was supported up front by Harry Yorston.