In 1964, Conroy was offered a contract at Shelbourne and Shamrock Rovers. However he instead moved to Northern Irish club Glentoran, where he believed that he would have a better chance of being spotted by an English club. He received a signing-on fee of £600. As the club were based in Belfast he had to spend the night at manager Billy Neill's house after midweek games as he would miss the last train back to Dublin, and would have to instead catch the train the following morning to make it back to his regular job as a printer. He played for the Glentoran 'Seconds' (reserve team) in the final of the Steel &amp; Sons Cup on 25 December 1965, which ended in a 1–0 victory over Larne. He scored on his first team debut two days later, a 3–2 win over Bangor. He went on to score both goals for Glentoran in the Irish Cup final on 23 April 1966, a 2–0 win over Linfield at The Oval. In total he scored eight goals in the 1965–66 season, as the "Glens" finished third in the Irish League, two points behind champions Linfield. He went on to score 25 goals in the 1966–67 campaign, as Glentoran won the league by a one-point margin. He also played in Europe, as the Irish Cup win also qualified Glentoran to a place in the European Cup Winners' Cup in 1966–67, and he helped the club to a 1–1 draw at home with eventual runners-up Rangers before they suffered a 4–0 loss at Ibrox Stadium. He received a league winner's medal despite leaving the club before the end of the season.