Prior was dropped for Bairstow for the fourth Test in Melbourne after an indifferent series but his understudy gave a mixed performance, dropping a catch and failing to respond to a snick from Chris Rogers when he was on 19, with the opener going on to score a century.
Clarke said Prior's vast experience was needed by England as they seek to deny Australia a 5-0 whitewash in Sydney, but Cook said Bairstow would get another chance as wicketkeeper.
Australian captain Clarke said England missed the big-match experience of Prior, who has 75 Test caps.
"I would be surprised if Matt Prior doesn't get recalled back into their team. Being a senior player with the amount of experience he has, I think they've certainly missed that," Clarke said at his media conference on the eve of the Test.
"He's been an important player for England over a long period of time. I think you can see the benefit of (wicketkeeper) Brad Haddin in our team, just with his experience," he added.
"He's still a fantastic cricketer, he's 31. He's still got a lot of Test cricket available to him if he wants it," the England captain said.
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