James William Keith Chapman, 37, was jailed for four months in May, 10 weeks in September and now another four months.

He was sentenced in the Launceston Magistrates Court on Monday after pleading guilty to evading police, resisting police, possessing stolen property, driving unlicensed and other offences.

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It was the second time this year Magistrate Sharon Cure has sentenced Chapman, saying it was a difficult case.

"It's just a revolving door, we're not getting anywhere, are we?" she said.

"It's really hard to manage him.

"He can't be placed on a corrections order, it's not a matter of giving him a suspended sentence. He does time for his crime, and don't crash him."

The court was told Chapman does not have a stable address and community service providers were struggling to assist him when he leaves custody.

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He was arrested and charged on December 1 after police spotted him driving a stolen Mitsubishi Pajero in Newnham. He drove away from police when they attempted to intercept him, only for him to park in a nearby street where he was arrested.

He was in possession of 11 bottles of veterinary drugs including ketamine and Diazepam which were later reported stolen from a vet clinic in Deloraine - a crime police did not allege he committed.

Chapman was released on bail to an address in Deloraine, but when they checked the address the following evening, the occupant said Chapman had never arrived there.

When he was arrested again on December 11, Chapman became agitated with police at the station and punched a protective screen around a custody officer. He resisted efforts to be handcuffed and was pinned to the ground.

The court heard he did not have a recent prior history of assaulting or resisting police, and officers were not considered at risk around him.

Chapman was jailed for four months from December 11.