I understand that the deputy is referring to Higher Education Institutions (HEIs) only in this question.
The position is that HEIs are autonomous institutions and it is a matter for the individual institutions to manage staffing and recruitment subject to compliance with the Employment Control Framework which limits the overall numbers employed in the sector. Under the terms of the ECF the HEIs are required to report wholetime equivalent permanent and temporary staff numbers on a quarterly basis. The particular information requested on those employed in the HEIs on contracts of indefinite duration is not available.