The procedure for applying for relief from customs duties and VAT on transferring residence to Ireland can be found at http://www.revenue.ie/en/customs/leaflets/pn1875.html and the procedures relating specifically to relief from VRT are at http://www.revenue.ie/en/tax/vrt/leaflets/tax-relief-transfer-residence.html.
The information supplied on the revenue website is primarily designed for persons who are moving house, with considerable belongings being shipped rather than carried as luggage. In most such cases, a customs agent is used to arrange the shipment, and the agent will be able to deal with any formalities. Duty and VAT do not normally arise, unless there are high value items which are capable of resale. For personal luggage such as would be carried by a normal passenger, no advance customs declaration is required.
In this case, it appears that a motor vehicle is being imported. Vehicle Registration tax (VRT) may be waived as described in the leaflet referred to above, which also provides contact details for further information. The claim for relief should be made at the local Revenue office within seven days of the arrival of the vehicle. It will be necessary to show that the vehicle was owned and used abroad for at least six months; that the person concerned resided abroad for at least one year; and that the person is now transferring permanent residence to Ireland, or has transferred residence within the previous year.