Premier Dominic Perrottet was asked about Amy Brown, a day after it was revealed she had relinquished her role as CEO of Investment NSW, but remained secretary of the Department of Enterprise, Investment and Trade.
"If there are ways in which we can do things better and have the right personnel in place from a public service standpoint that provides the right structure, then we should support that," the premier told reporters on Wednesday.
Mr Perrottet was also non-committal on whether Ms Brown should stay on as secretary of the Department of Enterprise, Investment and Trade.
"It's a matter for the public service in relation to that determination," he said.
Ms Brown was named in an independent review conducted by former NDIS commissioner Graeme Head.
He criticised her involvement in the appointment of Mr Barilaro to the $500,000 a year US trade job and recommended consideration be given to taking action against her.
The review found Ms Brown had been indirectly influenced by then-trade minister Stuart Ayres' preference for who took the New York-based role.
She was due to face a budget estimates hearing next week, but will not appear as she is on four weeks leave.
A department spokesperson said Ms Brown relinquished the CEO job on August 11.
"These roles have been separated to allow the secretary to focus on a cluster leadership role and an Investment NSW CEO to focus on the core activities of investment attraction," the spokesperson said.
"Due to the scale and significant nature of the work involved in both positions, the role of Investment CEO has been separated out from the secretary role description, title and accountabilities."
A Department of Premier and Cabinet spokesperson said department secretary Michael Coutts-Trotter had begun "formal discussions" with Ms Brown following the review.
"That process has been paused for four weeks as Ms Brown has taken leave following the intense public examination of her role in the STIC Americas recruitment process," the spokesperson said.
"Her privacy should be respected at this time."
Mr Ayres resigned as minister earlier this month after a draft excerpt from the Head review raised questions about whether he breached the ministerial code of conduct with his involvement.
The review into the bungled appointment found Mr Barilaro's employment was not kept at arm's length from government.
Mr Perrottet said the appointment process was "flawed from the outset".
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