Buckley suffered a slow start to the following season, with injuries meaning he did not make his first appearance until 29 November 2013 when he was a replacement against Edinburgh in the 2013–14 Pro12. His next game came in that season's Heineken Cup, where he came on from the bench in a famous victory over four time European champions Toulouse in France. He appeared in four of Connacht's pool games in the Cup, being a replacement on each occasion. In February 2014, Connacht's first choice loosehead prop, Brett Wilkinson, suffered a neck injury against Saracens, which ultimately forced him to retire. This saw Buckley play more frequently for the province, starting all but two of Connacht's remaining matches and featuring as a replacement in the others. Buckley made a total of 14 appearances in the 2013–14 Pro12, six of these coming as a replacement.