In 1972 Gleghorne made her senior debut for Ireland against Scotland. At the time she was still a sixteen year old schoolgirl at Ballymena Academy. In 1972–73 she scored the winning goal for Ireland against England at Wembley in front of a crowd of 60,000. In 1977 she was a member of the Ireland team that won the Triple Crown. She captained Ireland when they won the 1983 Intercontinental Cup in Kuala Lumpur. Her Ireland team mates from this era included Mary Geaney. She also represented Ireland at the 1984 Women's EuroHockey Nations Championship and the 1986 Women's Hockey World Cup. In 2010 she was inducted into the Irish Hockey Association Hall of Fame. She retired from the Ireland squad in 1986–87.