Brought up in Stewarton in East Ayrshire, Scotland, Reilly began her footballing career at age seven with local boys' club Stewarton United and at one point attracted the interest of scouts from Glasgow side Celtic. She made her debut for the women's side Stewarton Thistle Ladies in 1965 against the Johnston Red & White Rockets. She also competed in Hughie Green's Women's Football Tournament reaching the regional final, she was also part of the Stewarton side which lifted the inaugural Scottish Cup in 1971 and reached the first WFA Cup final the same year. In 1972 she moved to Westthorn Utd where she won the treble of Scottish Cup, League Cup and the first League championship. Westthorn also reached the WFA Cup final losing 2–0 to Southampton. A desire to play football professionally saw Reilly move to French professional ladies' side Reims in 1974. The Scottish Women's FA had reacted to criticism from Reilly and two other players, Edna Neillis and Elsie Cook, by banning them sine die. After a six-month spell with Reims, Reilly was bought by A.C.F. Milan and played for the women's professional team for four years, winning two league titles in the process. Following on from her initial spell with Milan, Reilly continued to play in Italian football until the age of 40, including spells with the ladies' sides of Catania and Lecce. Reilly twice won the Serie A Golden Boot during seasons 1978 and 1981, scoring 43 and 45 goals respectively. In the 1978–79 season she won championship titles in both Italy and France, playing for Lecce on a Saturday night and then flying to France to play for Reims on Sunday afternoons. She eventually retired aged 40, having won eight Serie A titles, a French title and four Italian Cups.
International career
Despite having played ten times for her native Scotland and having no formal links to Italy prior to her move to A.C.F. Milan, Reilly was selected for the Italian women's national team and was voted the best player in the Italian team which won the Mundialito in 1984, an unofficial precursor to the women's world cup. It was reported that team captain Reilly scored in the 3–1 final win over West Germany in the northern Italian town of Caorle. At the 1985 edition of the Mundialito, Reilly featured in Italy's 1–0 win over the United States women's national soccer team, substituting in for Viviana Bontacchio on 63 minutes. It was the American team's first ever appearance at international level.