The gallery entered into an agreement to give the money up front to Sean Rainbird when he took up the position last year.
But the payment was made without the permission of the Department of Public Expenditure.
Gallery chairman Olive Braiden told the Dail spending watchdog, the Public Accounts Committee, the payment was to allow Mr Rainbird to travel to see his family in the London 40 weekends a year at a cost of €200 per round trip over the five years of his contract.
It was part of an agreement entered into him when Mr Rainbird agreed to move to Dublin from Stuttgart, where he had been the director of the Staatsgalerie.
Independent TD Shane Ross told the committee: “This is a top-up in effect.”
She said it had paid a reasonable expense to ensure that an overseas candidate would not be "worse off" during the five-year contract for the job.
The committee heard the full cost of the payment to the taxpayer was actually €87,500 after the gallery received advice tax was payable on the allowance.