Most EU countries have withholding tax obligations, similar to PAYE, and depending on each country's domestic tax rules if you are not tax resident in that country you may be able to reclaim the withholding tax as a non-residnet. However, you will need to prove payment of tax in Ireland.
In most countries, if you spend at least 183 days a year there you will be tax resident there and have to pay tax in that country.
If you do not break Irish residence, you will have to pay tax in Ireland also, but will get a credit in Ireland for the foreign tax paid, or may be able to reclaim tax in the other country due to dual residence depending on the terms of the Double Tax treaty, but will need to take advice in that country as to how to do that.