Career
Club
Grierson started out at Queen"s Park before then manager Bill Struth brought him to Rangers in 1952. He made his competitive debut in a 5–0 defeat to Hearts on 9 August. He scored his first and second goals for the club a week later in a League Cup match against Aberdeen.
Those goals were to be some of many.
In his four seasons at Ibrox he netted 59 times in total. He was Rangers top scorer in his first season after scoring 31 goals.
He is noted as scoring the first ever live goal on Scottish television He scored 23 league goals for the Bairns but left them in 1960 to join Arbroath.
He retired to Newton Mearns, in East Renfrewshire.
Derek died on 7 September 2011, aged 79. At the Falkirk v Rangers Scottish League Cup third round match, played on 21 September 2011, Grierson was remembered during a minutes silence at the beginning of the match, in memory of his contribution to both clubs during the 1950s
International
As an amateur, he was selected for trials for the Great Britain side that was to take part in the Helsinki Olympic Games of 1952. Manager Walter Winterbottom was duly impressed and Grierson made the squad - one of only three Scots selected.