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Deans had a big supporter in former boss John O'Neill, but new man Pulver has suggested the former Crusaders coach might not have it all his own way.
However, any changes will be kept to a minimum while Pulver, who has never worked in sports administration, settles in.
Deans has said he wants to keep his position through to the 2015 World Cup in England and has already told Pulver, who was appointed on Wednesday, of his intention.
At a press conference to announce he was succeeding John O'Neill as the ARU's boss, Pulver said Deans was not under threat to keep his position for the remainder of his contract, during which the Wallabies will play 14 tests, including three against the British and Irish Lions.
Asked if Deans would have to reapply for the Wallabies coaching job if he wants to continue in it, Pulver said: "Yes."
Deans has coached the Wallabies since 2008 and, before last year's World Cup, had his contract extended. But recently he has come under scrutiny as the Wallabies dropped a place to No3 in the world rankings. He has also clashed with Quade Cooper and fellow first-five Matt Giteau, who is no longer in the Wallabies set-up.
"There is no question that Robbie, and I am sure a number of other coaches, will really want to take the Australian rugby team right through to the 2015 World Cup," Pulver said.