MARINE ecologist Dr Danny Bucher said it sounded like a great white shark's behaviour at The Pass was escalating and could pose a danger.
Dr Bucher, from Southern Cross University's Marine Ecology Research Centre, said it may lead to an attack.
"If he's getting bolder and bolder ... it may turn into a bite," Dr Bucher said.
"It's very unusual behaviour.
"It does sound like he's trying to scare them off.
"This is the kind of move that sharks make to scare off other sharks.
"It's 'get out of the way, this is my area'. He's treating them as potential competitors.
So if he's hanging around I'd be getting out of the water. It's not a time for panic; it's a time for caution.
Dr Bucher said scaring off the shark with a jet ski would probably be the best way to address the issue if its menacing behaviour continued.
He said swimmers inside the surf break were not those at greatest risk as great whites were too big to come in close.
"The surfers and the off-shore swimmers, they're the ones who really have to look out."
Jim Keough, the emergency services co-ordinator for Surf Life Saving Far North Coast, said he had heard rumours of the sharks but had received no formal notification, which was necessary for them to act.
Mr Keough, who is also a member of Byron Bay Surf Life Saving Club, said shark sightings should be reported to 000.
Surf Life Saving said they would also report the shark to Marine Parks, particularly in the lead-up to the busy Schoolies period.
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