She resigned as the committee's vice president after two years in the role.
In a States debate on Wednesday morning, Deputy Murray received 20 votes while 17 States members backed challenger Deputy Gavin St Pier. There was one spoilt paper.
With Deputy Murray stepping up to the Policy & Resources committee, Guernsey's Education, Sport and Culture committee and Development and Planning Authority both have vacancies.
Elections for those positions are likely to take place on Wednesday 14 December.