The Corrections Association is seeking to appeal against an Employment Court judgement in favour of extending double bunking in prisons.
Last month, the court rejected a case brought by the union, which argued its collective agreement would be breached by wider use of double bunking.
The association's president, Bevan Hanlon, says the judgement is wrong in law.
However, the Government says new court action will not stop its plans to increase the number of double-bunked cells at four of the country's newest prisons.
It says the Employment Court's finding stands, unless any appeal is successful.
