Gleghorne made his senior Ireland debut in June 2009 in a Celtic Cup match against France. Gleghorne and his fellow debutant, Chris Cargo, both scored in a 3–1 win for Ireland. Gleghorne was a member of the Ireland team that won the 2011 Men's Hockey Champions Challenge II. He also helped Ireland win Men's FIH Hockey World League tournaments in 2012, 2015 and 2017. Gleghorne was also a member of the Ireland team that won the bronze medal at the 2015 Men's EuroHockey Nations Championship. He also represented Ireland at the 2016 Summer Olympics In June 2017 he was a member of the Ireland team that won the Hamburg Masters, defeating Germany 4–2 in the final.