In order to work in Ireland a non-EEA National, unless they are exempted, must hold a valid Employment Permit. The Department of Enterprise, Trade and Employment administers the Employment Permits system. Detailed information on work permits, Highly Skilled Eligible Occupations List, etc. is available on internet websites:

https://www.irishimmigration.ie/coming-to-work-in-ireland/what-are-my-options-for-working-in-ireland/coming-to-work-for-more-than-90-days/

Employment Permits - DETE (enterprise.gov.ie)