The Public Service Act allows for inquiries into an alleged breach of the APS Code of Conduct by an agency head, an APS employee or former APS employee, but does not explicitly allow for former agency heads to be investigated.

The bill was amended in 2012 to include the term "former APS employee". At the time Minister Chris Evans told parliament the amendment aimed to make it "less attractive for employees who are under investigation to resign before a finding is made, as many employees in this situation currently do".

In reality investigations fall by the wayside if the employee under investigation resigns during the process.

The 2017 State of the Service report said that in approximately 15 per cent of the 596 Code of Conduct investigations in the previous year, an employee's resignation led to either the investigation being discontinued or no sanction being applied after a breach was found.

According to the report, in 14.26 per cent of cases, or around 85 individuals investigated, a breach of the Code of Conduct was found, but no sanction was applied because the employee resigned before a decision could be made. In 1.34 per cent of cases, or around eight individuals, the investigation was discontinued before a finding could be made because the employee resigned.

Acting merit protection commissioner Mark Davidson told a Senate estimates committee last month that he was yet to make a decision on whether to begin an investigation into Mr Lloyd. In the letter to the committee, Mr Davidson said he had originally decided to delay the decision so it could be referred to a permanent merit protection commissioner when appointed.

Mr Davidson would not comment this week on whether he had made a decision on whether to launch an investigation into Mr Lloyd.

Mr Davidson also did not comment on whether investigations in general were continued if the subject of allegations resigned.

Minister assisting the Prime Minister for the Public Service Kelly O'Dwyer announced on Friday that Linda Waugh had been appointed to the role of merit protection commissioner, to commence a five year term on June 25.

A spokeswoman for Ms O'Dwyer said the government had not yet made a decision on John Lloyd's replacement, or if the position would be advertised.

“The government is considering arrangements for a new appointment,” she said.

New ACT Labor senator David Smith has written to the minister, calling the recruitment of a new commissioner "a valuable opportunity to appoint someone who will carry out the functions of the position with integrity and impartiality".

Mr Smith said leadership in the public service should "[embody] the values expected throughout the service".

John Lloyd announced that he would retire from his role as Public Service Commissioner last week, but denied that the decision had been influenced by the possibility of an investigation into an alleged breach of the code of conduct.

He had been under pressure over his connection to the right-wing think tank the Institute of Public Affairs, after it was revealed at Senate estimates in October that he had sent an email to a member of the IPA with an attachment detailing provisions in public service agreements he described as "generous".

Throughout questioning in Senate estimates and in interviews since his resignation, Mr Lloyd has maintained that he did not act improperly in his contact with the think tank.