The Probate Act (1857) did away with the testamentary authority of the Church of Ireland. Instead of the Consistorial Courts and the Prerogative Court, power to grant probate and issue letters of administration was vested in a Principal Registry in Dublin and eleven District Registries. Rules similar to those governing the geographical jurisdiction of the ecclesiastical courts applied, with the Principal Registry taking the place of the Prerogative Court, as well as covering Dublin and a large area around it. Transcripts of the wills proved and administrations granted were made in the District Registries, and the originals were forwarded to the Principal Registry. Almost all the records of the Principal Registry were destroyed in 1922. The Will Book transcripts made by the District Registries did survive, however. The records of those districts covering areas now in the Republic - Ballina, Cavan, Cork, Kilkenny, Limerick, Mullingar, Tuam and Waterford - are in NAI and online (see the checklist here). For districts now in Northern Ireland - Armagh, Belfast and Londonderry - the Will Books are in PRONI and are searchable through the PRONI website.
Fortunately, from 1858 a new system of indexing and organising wills and administrations had been devised. A printed, alphabetically ordered Calendar of Wills and Administrations was produced for every year, and copies of all of these have survived. For each will or administration, these record:
In many cases the relationship of the executor is also specified. This means that, despite the loss of so much original post-1857 testamentary material, some information at least is available on all wills or administrations from this period. Very often, much that is of genealogical value can be gleaned from the calendars, including such information as exact dates of death, places of residence and indications of economic status. An index of testators and executors linked to images of the corresponding Calendar page is online at genealogy.nationalarchives.ie . It is complete only up to 1917, because this is the last year of the LDS microfilms on which the index is based. After that year it is necessary to consult the calendars on open access in the NAI reading room, with a copy also in PRONI. Calendar entries relating to the three district registries of Armagh, Belfast and Londonderry are searchable at nidirect.gov.uk/proni up to 1921, when partition made it necessary to redraw the registry boundaries. For areas in Northern Ireland the PRONI online search comes up to 1965.
A detailed guide to the post-1858 Calendars in both Northern Ireland and the Republic is on the website of the Council of Irish Genealogical Organisations. Links to the post-1922 Calendars for the Republic are also here.