There are several circumstances in which young foreign national persons may be in the State in full time education. The most obvious would be as an international student. The Immigration and Naturalisation Service has comprehensive guidelines on student migration (http://www.inis.gov.ie/en/INIS/Pages/Students) which clearly set out the circumstances in which a person may take up residence in the State as a student.
Young persons might also be in full time primary or secondary education in the State as the family member of certain classes of persons who have permission to reside in the State. It does not follow, however, that such non-nationals residing in the State have an automatic right to access State-supported education, particularly at tertiary level. For example, the children of a person working in the State on an employment permit may not be able to avail of State-supported university education for his or her children, and will be required to pay international fees. This is the policy position relating to access to state-supported education by non-EEA nationals generally (young persons recognised as refugees excepted).
I should add, of course, that policy generally in relation to access to full time education in the State is the responsibility of my colleague the Minister for Education and Skills.