Clancy was encouraged to become a rugby union referee by his father. Seoirse Clancy was involved with Bruff R.F.C. and had refereed at a local level. He encouraged his son to take up refereeing after injuries, including a broken leg, prevented him from playing rugby union at a top level.[1][6][7] In October 2000 Clancy refereed his first match, an U15s league match between Richmond and Garryowen which ended in a 0–0 draw.[5][11] He subsequently began refereeing games in the All-Ireland League[8] before making his Celtic League debut on 15 October 2004 when he took charge of a match between Borders and Gwent Dragons.[6][7][11][12][13]
During his refereeing career Clancy has been involved in several controversies and incidents. On his Six Nations Championship debut on 14 February 2009, Clancy awarded a try to France's Fulgence Ouedraogo against Scotland. Replays showed the final pass from Maxime Médard was forward. However, Clancy had been knocked to the ground in the move building up to the score. He consulted with his assistant before confirming the try.[20][22]
On 5 December 2009, after refereeing an All-Ireland League match between Shannon and Cork Constitution, Clancy was verbally abused by Shannon supporters and club officials. Among the alleged abusers was Gerry McLoughlin. After the match had finished Martin Clancy, the Shannon president, entered the referees dressing room and continued to verbally abuse the referee. He was eventually removed by the two touch judges. Shannon were subsequently fined €25,000.[24]
On 13 February 2010 during a match between Wales and Scotland, Clancy sin-binned Scotland's Phil Godman for an alleged off-the-ball trip on Lee Byrne. Byrne was later accused of deliberately diving to help Wales win.[22][25][26]
On 10 April 2010, during a 2009–10 Heineken Cup quarter-final, between Biarritz and Ospreys, Clancy refused to award Ospreys a penalty towards the end of the match after an alleged knock-on by Biarritz's scrum-half, Dimitri Yachvili. The decision denied Ospreys a potential victory.[19][22][27]
On 6 September 2014 Clancy refereed a match between Australia and South Africa. Clancy yellow carded South Africa's Bryan Habana for a high tackle on Adam Ashley-Cooper in the 65th minute. According to Paul Cully of The Sydney Morning Herald
the decision was incorrect and was "the defining moment" of the match, costing South Africa a potential victory.[28][29]
On 16 September 2017 Clancy was serving as a touch judge during a 2017–18 Pro14 match between Cardiff Blues and Glasgow Warriors. A disgruntled Cardiff Blues fan threw his pint of beer at Clancy because he allegedly was unhappy with a decision made by the officials. The act was caught on camera and the fan was quickly escorted from the ground.[30][31]