The government has advertised for the head of the new HSE board which will be responsible for choosing Tony O'Brien's replacement.
The government intends to establish a board to have more oversight over the performance of the health service.
The successful candidate for chairperson will get €80,000 a year for up to two days of work a week.
The board will be the new governing body for the HSE.
Minister for Health, Simon Harris, has welcomed a new recruitment campaign to select a Chairperson for the new HSE Board.
Minister Harris said: "The Chairperson will be responsible for leadership of the HSE Board and will play a key role in establishing the Board governance structures and ensuring their effective and cohesive operation.
"The new Chairperson will play a central role in relation to the direction, leadership and corporate and clinical governance of the HSE, during a period of complex change.
“The legislation to establish a Board for the HSE is being drafted as a priority and I intend to publish the Bill in July and bring it through the Oireachtas early in the Autumn/Winter session.
"It is my intention to establish the Board once the legislation has been passed.
"Under the new legislation the Board will be accountable to the Minister for the performance of its functions and it will be responsible for the appointment of a CEO.
"The CEO will be responsible to the Board and the Board will take responsibility for assessing the CEO’s performance.
"I firmly believe that the appointment of a strong Board, with a strong Chairperson, will help ensure robust governance of the HSE."