When you arrive in Ireland you will be given:
Leave to enter Ireland.
Permission to Remain for a particular purpose allowing you to remain for a period (which may be up to three months).
If you wish to remain beyond the period granted by an Immigration Officer, you are required to obtain the permission of the Minister for Justice and Equality.
This can be done by reporting to your local Superintendent’s Office in An Garda Síochána (Irish Police) in the district in which you reside.
In Dublin, you must report to the Garda National Immigration Bureau.