Heenan signed on a three-year contract for Irish provincial side Connacht in May 2013, joining the team for the 2013–14 season. He joined former Blues coach Pat Lam, who had been appointed as the team's head coach. Heenan made his debut for the side on 7 September 2013, coming off the bench against Zebre in the Pro12. His first start came in an Irish provincial derby with Ulster, where Heenan played the full 80 minutes. He made his Heineken Cup debut on 11 October 2013, starting against Saracens. He was named as Connacht's player of the month for October 2013, only one month after his debut. Heenan played the full match at openside flanker for Connacht as they produced one of the biggest shocks in the history of the competition, beating four-time champions Toulouse in the pool stages in the Stade Ernest-Wallon. He made a total of 12 league and six European appearances in his first season, but missed the second half of the season after suffering a shoulder injury against Saracens in January 2014.