A proposed new law could see governors-general accused of serious misconduct stripped of their allowances.

Greens Senator Rachel Siewert is introducing a private member's bill aimed largely at former governor-general Peter Hollingworth.

Dr Hollingworth quit in 2003 after it was revealed that he allowed a known paedophile to stay on as a priest while he was the Anglican archbishop of Brisbane.

Dr Hollingworth still receives a $357,000 annual pension plus travel and office expenses, despite being head of state for less than two years and being forced to leave in disgrace.

Senator Siewert says there is a clear oversight.

“It is important that people who hold public office are held accountable,” she said.

Lisa Flynn, lawyer for victims of abuse by priests, says survivors and their supporters want those who facilitate child sex abuse to face the consequences.

“There's a hugely strong sentiment that people who cover up child sexual abuse, who don't report it, who don't stop it when they have an opportunity to do so, should actually be punished,” she said.

“Rather than continue to reap the rewards of the position that they were in when they allowed the abuse to continue.”

Ms Flynn believes almost no taxpayers would be happy with having to fund Dr Hollingworth’s lush lifestyle.

“I think that it would come as a surprise to many people when it was very public, in terms of his failings towards children that were vulnerable and that were being sexually abused,” she added.

“I do think that it's an incredible sort of sum for anyone to receive, but particularly when someone has acted like that in their career.”

The explanatory memorandum for the Greens’ bill defines serious misconduct as inappropriate, improper, wrong or unlawful conduct, or a failure to act.

The bill says this could include corruption, sexual misconduct, sexual harassment, theft, fraud and other criminal behaviour.