registration to work

If you intend to stay longer than 3 months, that is permanently, you have to register within those 3 months not after the 3 months is up.

Been posted many times and John123456 has give loads of links on how to do it but you need to make an appointment with various National Police stations to obtain an NIE which is a foreigners' ID number, a bit like the UK NI number. You then need another appointment to go on the register of foreign EU residents living in Spain. 

All appointments can be made via this link Cita Previa and selecting the province you are going to live in

As an EU citizen you do not need a work permit and can look for a job without notifying or registering. Of course, you will be registered with the Tax office when you do start work. 

yes we both have nie from property purchase.

I know it can be done areself but woukd you suggest using an agent as spanish would be great.

As marcliff has already alluded to there are numerous posts on this Forum containing information about registration with the Spanish authorities for foreign nationals. If you have a good command of Spanish you can go through the registration for foreign nationals process yourself otherwise you will need an interpreter but you must attend the appointment in person.  

You mentioned you wish to work in Spain and if you haven't a job already lined up you may be interested in the following:

The Department for Social Protection in the RoI have EURES Advisers who are trained specialists and provide the three basic EURES services of information, guidance and placement, to both jobseekers and employers interested in the European job market. They have developed specialised expertise in the practical, legal and administrative matters relating to mobility at national and cross-border levels.

EURES Ireland (EURopean Employment Services) is part of a network of more than 1,000 EURES Advisers across Europe.

EURES Advisers provide information, guidance and recruitment services to both jobseekers and employers interested in the European job market.

EURES was established by the European Commission to facilitate the free movement of workers within the European Union (EU)/European Economic Area (EEA) countries.

The following links will provide greater detail:

https://www.gov.ie/en/publication/d9a16c-eures-advisers/?referrer=https://www.welfare.ie/en/Pages/EURES-Advisers.aspx

https://www.gov.ie/en/campaigns/d6aa7d-eures-ireland/

home?lang=en

https://europa.eu/eures/port

Residency and entry requirements
EU citizens who wish to reside in Spain for less than three months do not need to apply for a registration certificate. Only those who want to reside in Spain for more than three months have to apply for a Certificate of Registration in the Oficina de Extranjeros (Foreigners Office) or if there is none in your region, at designated police stations. A list of Foreigners Offices is available on the website of the 

Dependencias. Sitio web de la Policía Nacional España (policia.es).

This link will provide you with further information:
https://www.ireland.ie/en/spain/madrid/services/new-to-spain/#:~:text=Only%20those%20who%20want%20to,the%20website%20of%20the%20Dependencias.

If you need any further information please don't hesitate to ask.