Grealey first represented Ireland Women in 1985, appearing in Ireland's first ODI in 1987 before becoming captain in 1995. Her playing career continued until 2005 and included 79 ODIs as well as captaining the side in Ireland Women's only Test, played against Pakistan in 2000. Despite retirement, Grealey's involvement with the national team persisted through her roles as Team Manager, coach and latterly Chair of National Selectors.

Grealey took 38 ODI wickets, as well as scoring one hundred and five fifties

Asked about her favourite memories from her playing days, Grealey recounted her ODI hundred made against Pakistan as standing out, as well as the 57 she made against Australia "solely because I had to face Cathryn Fitzpatrick and my teammates all knew I preferred slow bowling to quickies." She added, "I was fairly black-and-blue by the time she had finished her spell, so it was without exception my best battling 50! I guess though my proudest moment was winning the European Cup with Ireland in 2001, our first major trophy beating England in the final."

She has taken the decision to step down as a national selector in order to allow someone able to commit more time to the role to fill her position.

"Being a national selector is a big commitment," she said in a press statement. "I don’t attend many winter net sessions, as I know this is the time the girls are working on correcting parts of their games, and don’t need me standing there looking over them. Once the season gets underway, we try to cover as many games as possible. Basically, I then inform the other selectors and coach about certain players we were keeping an eye on. Statistics can lie, so it’s important to watch the game. Scoring big doesn’t mean you weren’t dropped a few times or played poor shots. Equally, good bowling figures means very little, unless you see ‘how’ they bowled. I guess I can’t commit that time anymore and is one of the reasons I’m stepping down as selector - the girls work too hard not to have a selector who’s totally committed."

Former Ireland batsman, and now Ireland Women coach, Ed Joyce took to Twitter to praise Grealey, while Cricket Ireland's Performance Director, Richard Holdsworth, hailed Grealey as a "legend of the Irish game" and was glowing with praise for the impact she has had on cricket in the country.

"Her passion for cricket, her experience and her insights have helped in the development of generations of Irish cricketers," he said. "Throughout the many roles she has undertaken, Miriam has been a role model for many, and an ambassador for all. While we will miss her contributions at an official level, she will undoubtedly continue to be a regular supporter of our national sides, and an advocate for the women’s game in this country."