The Minister for Finance has told the Dáil that "huge engagement is underway" to manage the exit of Ulster Bank and KBC from the Republic.
Paschal Donohoe told Fianna Fáil's Brendan Smyth that the Central Bank has met the banks who were involved, both those withdrawing and those remaining.
It is a "a moment of huge change" for customers, he said.
"This is a transition that we need to go well," he added.
The union has commissioned a survey of its members, which shows that 88% of respondents feel stressed at work either on a regular or very regular basis.