Scott Morrison’s communications director has resigned after a dispute between the Turnbull government and the Australian Bankers’ Association over the appointment of former Labor Queensland premier Anna Bligh.

The treasurer’s communications director, Sasha Grebe, has left his job after reportedly applying for the ABA chief executive’s role, which was handed to Bligh last week.

A spokesman for Morrison said Grebe had been seeking positions in the corporate sector “since last year’s election”.

“Sasha Grebe has left the treasurer’s office,” the spokesman confirmed. “The treasurer wishes him well in his future endeavours.”

Grebe’s phone has been disconnected. The Turnbull government was upset last week by news the ABA had appointed Bligh as its new CEO.

After the ABA’s announcement, Bligh put herself at odds with the Labor leader, Bill Shorten – who has repeatedly called for a royal commission into the banking industry – by saying a royal commission was not necessary.

“I think it’s clear the government has heard those calls and that’s why they’ve established a number of enquiries that are currently under way,” she said.

Despite her opposition to a royal commission, some Turnbull government MPs are still annoyed about her appointment.

The Liberal party frontbencher Zed Seselja has accused the ABA of trying to “appease” Labor by appointing Bligh, while Morrison has questioned why the ABA would want to be led by a former Labor premier.

“It’s not for me to be happy about it or not happy about. I will simply deal with whoever they put up,” Morrison told 2GB radio on Monday.

“I will continue to deal with the ABA professionally as I always have regardless of who is in that job ... [but] in all of my engagements with the banks, they’re mainly directly with the banks themselves, I don’t need to work through an intermediary,” he said.

Some government MPs last week called for the big four banks to be excluded from the government’s planned $48bn tax cuts after the ABA appointed Bligh as CEO.

Morrison’s senior media adviser, Julian Leembruggen, will be acting in the strategy and communications roles.