After her children were grown up, Squire enrolled at
Carleton University in Ottawa and received her B.A. in 1974, and an M.A. in Religion in 1975. She then taught at Carleton's Lay School of Theology from 1975 until 1982. In 1982, she was appointed Secretary of the United Church Division of Ministry, Personnel and Education. The committee recommended a church-wide study, which was implemented. As part of her final days as Moderator, Squire presided over the 32nd General Council of the United Church, where the report
Gift, Dilemma, and Promise: A Report and Affirmations of Human Sexuality was received. The report stated that "all persons, regardless of sexual orientation, who profess their faith in Jesus Christ are welcome to be or become members of The United Church of Canada" and that "all members of the United Church are eligible to be considered for ordered ministry." After much debate, the report was accepted, opening the door to ordination of members of the LGBTQ community. Of her time as Moderator, a role traditionally filled by an ordained minister, Squire wrote, "My theology of ministry is that all ministry is the ministry of Jesus Christ, and we are invited to participate in that. Lay people have as much to offer as those in the Order of Ministry. All that I have done is to help that concept of ministry be accepted by the church." ==Honours==