Fairbrother first competed internationally at the 1958 British Empire and Commonwealth Games in Cardiff, Wales. Representing Scotland, he finished in seventh place in the final of the high jump with a jump of . One month later at the 1958 European Athletics Championships in Stockholm, Sweden, Fairbrother, representing Great Britain in the high jump, finished tenth in the final clearing . At the 1960 Summer Olympics in Rome, Fairbrother failed to make the qualifying height of in the high jump. Two years later at the 1962 European Athletics Championships in Belgrade, Yugoslavia, Fairbrother in the high jump cleared . Two months later at the 1962 British Empire and Commonwealth Games in Perth, Western Australia, Fairbrother finished eighth in the high jump clearing the bar at . At the 1966 British Empire and Commonwealth Games in Kingston, Jamaica, Fairbrother recorded his best international result finishing fourth in the high jump clearing the bar at . At his final international meet, the 1970 British Commonwealth Games in Edinburgh, Fairbrother took the oath of behalf of the competitors at the opening ceremony. The following day in the high jump, Fairbrother failed to make the final.