Hi.
If you are the importer of record in to Ireland then you would need to register for VAT in Ireland and you would then be able to recover the import VAT paid on the Irish VAT return.
If you are not the importer of record in to Ireland then you would not be required to register for VAT in Ireland and therefore there be no facility to be able to recover the import VAT incurred.
There is a process for recovering VAT incurred in member states but you would need to mjeet the cinditions set out for a particular memeber state.
Please see the guidance below:
How UK and Isle of Man businesses can claim overseas VAT