Typically if you purchase a vehicle in Northern Ireland and import it to the Republic of Ireland you are not required to complete a customs declaration if the vehicle was first registered in Northern Ireland and never previously registered in the UK.
If you purchase a vehicle in the Northern Ireland that was previously registered in the UK and arrived in Northern Ireland after January 1st 2021 then you are required to complete a customs declaration when you import it to the Republic of Ireland.
You will need a customs agent to complete the customs declaration on your behalf. At CustomsDeclaration.ie we have successfully completed many customs declarations for people who have imported UK registered vehicles from Northern Ireland.
For more details go to Request a Customs Declaration.