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Divorce is not permitted in Ireland. It is however possible to get a annulment under certain restricted circumstances. Annulments only apply to religous marriages and not for civil ones.
If the husband is legally resident in the UK for a year he can apply for a divorce in the UK, which allows him to legally remarry in a civil ceremony in the UK. This option is not available to the wife [please correct me if anybody knows better].
An announcement on a divorce referundum is expected in the not TOO distant future.