The teacher-training college, the Marino Institute of Education, is said to be in crisis after the sudden resignation of its director, Caoimhe Mairtin.
The primary teachers' union, the INTO, wants an inquiry into the circumstances surrounding the weekend departure of Ms Mairtin from the north Dublin college, which is run by the Christian Brothers.
She had taken a High Court action against the trustees and governing body of the college, claiming she was bullied and subjected to intimidation.
A Christian brother who claims he was moved by the order is also calling for an inquiry.
The Department of Education has said tonight that it does not have any role in staff management but that correspondence it had received was under consideration.
