Sandra Pragnell, from the UK, said it was a special occasion in the historic 12th-century cathedral for both the Church of Ireland and wider community in Limerick and Kerry.
The ceremony was conducted by the Bishop of Limerick, Rev Trevor Williams, and the congregation included the Catholic administrator of the Diocese of Limerick, Fr Tony Mullins; the lay leader of the Methodist Church Gillian Kingston; retired Church of Ireland Archbishop of Armagh, Rev Alan Harper; and the retired Archbishop of Dublin, Rev Walton Empey, who ordained Dean Pragnell to the priesthood in the Christ Church Cathedral, Dublin.
The Mayor of Limerick, Cllr Gerry McLoughlin, led civic figures at the installation.
Dean Pragnell, from Hampshire, worked in the public sector in London before entering the ministry in Dublin, where she studied at Trinity College and All Hallows.
She said her ministry was about people, and she had spent a lot of time as a clergy woman working with immigrants in this country.
“People count, people need to know that they belong, whether they come to church, are occasional attenders, whether they are lapsed, whatever.
“They still belong, they belong to the church if they are baptised, they belong to the family of God. So people count and people matter.”
She said she looked forward to building up a working relationship with the Catholic Church in Limerick under Fr Mullins, adding: “That has happened in every parish I have been in and I think it is so important. The more we can do together, the more we are doing what Christ wants us to do.”
Having spent her ministry to date in Dublin and Dundalk, Dean Pragnell said she was looking forward to exploring Limerick and Kerry, new parts of Ireland for her.
“In my last parish I was the first woman rector. I was quite anxious before I went, knowing some people would have reservations having never had a woman priest.
“But the people were just fabulous and welcoming and so far here have been very welcoming also.”