The sitting member for Rosevears, Kerry Finch, says it will be "undemocratic' if two Upper House seats remain vacant until an election is held.
His view is supported by three independent Upper House members who have written to Premier Peter Gutwein saying it is not acceptable to leave the seats of Rosevears and Huon without a sitting MLC.
Mr Finch, who is retiring after 18 years, said he was prepared to stay on until an election was held even if that was until May 2021.
"It's all up in the air, but I'm happy to stay on as long as they need me," he said.
"It would be ridiculous to hold elections now when people are not supposed to travel and we have safe distancing.
"It seems to be a Constitutional stumbling block but it would be undemocratic to have 50,000 voters unrepresented until an election before August."
His views are echoed by the member for Launceston, Rosemary Armitage, McIntyre member Tania Rattray and Windermere member Ivan Dean.
They want the Premier to have a full postal vote or to recall Parliament to make changes to allow the incumbents to stay until there is an election.
"It is unprecedented that they won't have representation for an unknown period," Ms Armitage said.
"Legislative councillors look at local, state and federal issues and people come to us because we are the common people."
Ms Rattray said her office had been "flat strap" dealing with people's questions about COVID-19.
"People need support and a local member now more than ever because they are feeling uneasy," she said.
"They are talking about cancelling the Boxing Day cricket test so how can we be sure there will be an election before the end of August?
"We need a full postal vote option or to leave the incumbents there."
Mr Dean said his office had been "crazy" since the coronavirus. "I haven't stopped running all day," he said.
"The Legislative Council is part of our democracy and every Tasmanian deserves representation now."
Attorney-General Elise Archer has deferred the elections from May 2 until May 30 and said they would be held by the time the Legislative Council sits again on August 25.
She said the polls would be held when it was safe.
"Under the Constitution Act their terms expire at the end of May. There is no emergency power to extend these terms," Ms Archer said.
"That is why it is important to hold these elections as soon as is possible, but only when the risk to public health is reduced."
One political observer said there was no budget and no legislation so two fewer MLCs would not matter in the short term.