Centre Alliance Senator Rex Patrick will this week move to establish a Senate inquiry into the operation of the ministerial standards, saying Mr Pyne's appointment "doesn't pass the pub test".
"Neither Mr Pyne nor EY have been able to offer any convincing explanation as to how Mr Pyne's new job can properly be reconciled with the Prime Minister's Ministerial Standards concerning post-ministerial employment."
PM urged to act
Former ministers are banned for 18 months from lobbying, advocating or having meetings with members of parliament, the public service or defence force on any matters they officially dealt with while in office.
The guidelines are not enforceable but Senator Patrick has called on the prime minister to act.
"Mr Pyne cannot unknow what he knows from nearly three years’ service at the top of the Defence portfolio.
"His acceptance of his new job with EY is unquestionably a breach of the spirit, and indeed the letter, of the Prime Minister’s standards.
"The question is now that of what the Prime Minister is going to do about it."
Labor has also suggested Mr Pyne's new job is a breach of the standards and is considering supporting a parliamentary inquiry.
No code breach: Pyne
In a statement on Sunday, Mr Pyne said he was well aware of the ministerial rules and intended to abide by them.
"No one has been able to point to any instance of a breach of the code. Asserting something does not make it fact."
"Of course, I have 26 years of experience of the parliament... that gives me knowledge of government and politics and how it works that is valuable in the post political world. Having that knowledge does not breach the code."
Finance Minister Mathias Cormann appeared satisfied by Mr Pyne's reassurances that he would abide by the code.
"When members of parliament leave parliament obviously they've got to continue to work and not everyone can end up as a commentator on television," he told ABC radio on Monday.
Additional reporting: AAP