Bred at the Gerrardstown House Stud in Dunshauglin, County Meath, Our Conor was initially campaigned on the Flat by leading Irish jumps trainer Dessie Hughes, winning twice, at Roscommon and Naas, as a three-year-old, in the summer of 2012. Sent over obstacles that autumn, he made a winning debut in a maiden hurdle, again at Naas, justifying odds-on favouritism with an easy, 8½-length victory. He did so again in a Grade 3 juvenile hurdle at Fairyhouse the following month and, the following February, made a seamless transition to the highest level with a comfortable, 5-length defeat of the hitherto unbeaten Diakali, trained by Willie Mullins, in the Grade 1 Spring Juvenile Hurdle at Fairyhouse.
Our Conor subsequently arrived at the Cheltenham Festival boasting a 3-3 record over hurdles and, consequently, was sent off 4/1 joint second favourite for the Triumph Hurdle. Once again, he more than justified his market position, effortlessly drawing clear between the final two flights to win, impressively, by 15 lengths. Unsurprisingly, he was promoted to favouritism for the 2014 Champion Hurdle and, a few days later, sold to leading owner Barry Connell, for an undisclosed sum, although Connell declared himself ‘delighted to have the opportunity to buy him’.
The change of ownership meant that regular jockey Bryan Cooper, who had ridden Our Conor to all four wins over hurdles, was replaced by Danny Mullins, who was retained by Connell. Thereafter, barring a tenderly-handled fourth place on the Flat at Naas, the Jeremy gelding was campaigned exclusively at Grade 1 level over hurdles for the remainder of his tragically short career
However, he never won again. He was beaten by Hurricane Fly in the Ryanair Hurdle and the Irish Champion Hurdle, both at Leopardstown, before crossing swords with the defending champion for the third time in as many starts in the Champion Hurdle proper at Cheltenham. Sent off at 5/1 fourth favourite, he led as far as the third flight, where he took a horrific fall, sustaining a serious back injury. After extensive treatment by veterinary surgeons, he was humanely euthanised.