Charles Vincent Read, 23, who is in custody, appeared in Hobart Magistrates Court on Tuesday.
Police allege Read evaded police and failed to pull over when ordered when driving while disqualified at Bridgewater, north of Hobart, on February 15.
According to court documents, he was "careening" at speed in and out of lanes on a highway while all four tyres of his car were punctured.
It is alleged Read was found with the drug methylamphetamine and two unregistered guns, a Norica .22 calibre rifle and 303 British Savage Arms Lee Enfield bolt action rifle.
He is also accused of possessing ammunition when not the holder of the appropriate firearm licence and failing to take all precautions to ensure safekeeping of a firearm.
Read pleaded not guilty to all charges, apart from several breach of bail offences which were adjourned for mention.
He asked when he would be able to apply for bail but his lawyer Caroline Graves said he needed to get a few ducks in order first.
"There are a few chickens in the way at the moment," she said.
Read is expected to next appear in court on September 12.
Mark "Chopper" Read died in 2013 and was the subject of a film in 2000 about his life and time in prison.
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