Inheritance from someone in the EU

"Any foreign property will be taxable in cases where EITHER the disponer OR the beneficiary is resident or ordinary resident in Ireland at the relevant date. However, you may be entitled to a tax credit on the tax paid abroad to ensure you don't pay double tax."9 Mar 2020

MIght have been small changes since 2020 though I don't think so. Generally you won't be double taxed.

BTW the word you're looking for is hypothetical

If it's another EU country, then there is most likely no double taxation treaty term which applies, as Ireland only has such terms for the purpose of CAT in their US and UK tax treaties. As such, unilateral relief would apply for your Irish CAT liability; in essence, you can claim relief against your Irish CAT liability equal to the amount of foreign tax you paid on your acquisition of the foreign property in the country it is located in, thus avoiding double taxation. If there is no foreign tax liability on the inheritance, however (e.g. if the country in question doesn't have an inheritance tax, or the inheritance is below whatever their tax-free threshold would be under the current circumstances), then you would of course have no credit and you'd owe the full Irish CAT (taking into account any CAT relief you'd ordinarily be entitled to here, like your lifetime group thresholds).