Noelene June Jordan, 65, and Cedric Harper Jordan, 68, appeared briefly before Magistrate Michael Daly in Hobart on Monday afternoon to face the charges of murdering Mr Barker at his Campbell Town home on August 2, 2009.

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Mrs Jordan's legal counsel successfully sought a brief adjournment until June 4 for her client to enter a plea to the charge. Mr Jordan entered a not guilty plea to the charge and will appear in Launceston Supreme Court on July 20 at 9.30am.

Both were remanded in custody.

Mr Barker, 36, was found inside his Campbell Town home on August 3 with four gunshot wounds to his body.

Mr and Mrs Jordan were arrested by police at their Swansea property on Monday morning.

Acting-Assistant Commissioner Ian Whish-Wilson earlier in the day said the pair were known to Mr Barker.

"However, I'm not going to elaborate on the nature of their relationship," he said.

Acting-Assistant Commissioner Whish-Wilson said the arrests had followed a lengthy and extensive investigation into Mr Barker's death.

"These arrests are the culmination of a lengthy investigation by the Serious Organised Crime division of Tasmania Police," he said.

"The investigation has been complex and is one of Tasmania Police's longest running murder investigations."

Police offered increased a $50,000 reward for any information that could lead to a conviction for Mr Barker's murder to $250,000 in 2016.

This was the highest reward ever to be offered by Tasmania Police for information related to a case.

His father Robert Barker died in 2018 without knowing who had killed his son.

Mr Barker senior frequently spoke to the media about his son's death.

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