About three years after he was ordained a catholic priest by Dr. Ullathorne, vicar-apostolic of the western district, and on the restoration of the hierarchy in 1850 he was appointed æconomus of the diocese.
Bishop Ullathorne, in an address delivered on the occasion, pronounced a well-merited eulogy on Estcourt's 'assiduity, accuracy, punctuality, skill, and sound judgment.'
This controversial treatise by an erudite member of the Roman church, with a valuable appendix of original documents and facsimiles, appeared at a time when the vexed question of the validity of English orders was fiercely debated by members of the Anglican and Roman communions, and it attracted considerable attention (Academy, 26 April 1884).
An article, originally prepared by Estcourt for the 'Dublin Review,' was published separately instead, under the title, 'Dogmatic Teaching of the Book of Common Prayer on the subject of the Holy Eucharist,' 8vo.
Estcourt left unpublished a work of considerable interest, 'The Memoir of Jane Dormer, Duchess of Feria,' the materials for which he slowly accumulated during a period of twenty-five years.