The Senate has backed a push by the Centre Alliance’s Rex Patrick for an inquiry into the jobs taken by former ministers Julie Bishop and Christopher Pyne since they left politics at the May federal election.

Senator Patrick’s motion passed by 35 votes to 29 late on Monday after the crossbench, Labor and the Greens voted with Centre Alliance in favour of the inquiry.

The move came despite Australia’s top bureaucrat clearing the two former senior Liberals of any potential misconduct in their post-politics jobs on Monday.

Department of Prime Minister and Cabinet secretary Martin Parkinson reviewed both appointments and found ministerial rules had not been broken.

Mr Pyne has a new defence-focused role with professional services giant EY, while Ms Bishop has been appointed to the board of a foreign aid contractor.

Dr Parkinson has spoken to both former ministers in the past fortnight and reviewed arrangements with their new employers.

“Based on the conversation I had with Mr Pyne, I consider that he has put in place mechanisms to ensure that, while his engagement with EY will appropriately draw on his 26-year experience as a parliamentarian, he will not impart direct or specific knowledge known to him only by virtue of his ministerial position,” Dr Parkinson wrote in his report.

Prime Minister Scott Morrison told parliament on Monday, in response to a Labor question, he had accepted Dr Parkinson’s advice.

“I have no reason to doubt at all the competence of the secretary of the department in relation to these matters,” Mr Morrison said.

“All I can see is just another attempt by the Labor Party to get into … the chum bucket.”

Mr Morrison during question time on Monday. Photo: AAP

Mr Pyne’s engagement with EY is a six-month contract through public affairs consultancy GC Advisory, which he co-owns with his former chief of staff, Adam Howard.

He told Dr Parkinson he had made it clear to EY he could not lobby or meet defence portfolio ministers or department officials.

Similarly, Ms Bishop had assured Dr Parkinson she would comply with the standards.

She had no dealings with Palladium during her five years as foreign minister, she told him, and expects the company’s focus to be on projects in the US and Britain.

“Moreover, Ms Bishop has not been a minister for almost 12 months – a period in which certain elements of the aid program have been re-cast,” Dr Parkinson wrote.

Labor and some Senate crossbenchers raised concerns over jobs former defence minister Mr Pyne and ex-foreign minister Ms Bishop picked up after leaving parliament in May.

The ministerial code of conduct says ministers must not lobby or have business meetings with politicians or public servants within 18 months of leaving parliament, on matters they dealt with in their final 18 months in office.

Former deputy prime minister Barnaby Joyce would not be drawn on whether the jobs passed the pub test, saying: “Well, it passed the investigatory test.”

“Obviously I think that people rightly have questions that they want answered … about how you work for a defence organisation when you were the defence minister,” he said.

Dr Parkinson’s findings did not put One Nation leader Pauline Hanson’s mind at ease.

“He’s saying that all rules have been complied with. Maybe we should look at those rules,” she said.

“I have a grave concern about people who have held ministerial positions, dealt with companies that have received a million dollars, if not hundreds of millions of dollars in contracts, and now working for those firms?”

-with AAP