Workers at Permanent TSB who are members of the Unite union are lodging a claim for a 13% pay rise.
Unite, which represents a majority of workers at the bank, said the demand is in response to the ongoing rise in the cost of living coupled with PTSB's return to profitability.
The bank reported a full year profit before tax of €267m last year.
"In early August, when announcing the bank’s half-year profits, CEO Eamon Crowley signalled that PTSB may now be in a position to resume paying dividends," said the Unite General Secretary, Sharon Graham.
"PTSB’s recovery is thanks to the expertise and commitment of its workforce, and they must be first in line for a real dividend in the form of a cost-of-living pay increase."
"Our members are seeking a pay increase which reflects PTSB’s return to profitability and anticipated growth."
Unite added that those starting out in the bank and staff working in call centres have starting salaries of €27,500.
The union also wants pension contributions to increase, along with an extra day’s leave and a rise in maternity/paternity leave.
In March of last year, the bank agreed a pay increase of up to 6.5% over two years.
Starting salaries for entry level of graduate recruits also rose to the €27,500 mark from €25,000.
