The High Court has ordered recounts to replace former senate president Stephen Parry and former senator Jacqui Lambie, who both resigned when they found they were British citizens.

Each of the ex-senators resigned after unearthing details suggesting they were dual British nationals.

Mr Parry's most likely replacement is former senator Richard Colbeck, however below-the-line voting could complicate matters, as a quarter of all Tasmanian Senate votes were below the line.

Solicitor-General Stephen Donaghue told the court the process for determining Ms Lambie's replacement would be more complex, as her runner-up also faced eligibility questions.

Steve Martin was the Mayor of Devonport at the time of the election and may be disqualified from sitting in the Senate by another part of section 44 of the constitution, by holding an office of profit under the crown.

Justice Geoffrey Nettle said he had already thought about it and flagged a possible full bench hearing in late January.

Both cases will be back next Wednesday.

Kakoschke-Moore to fight for Senate return

Justice Nettle also considered the case of South Australian Nick Xenophon Team senator Skye Kakoschke-Moore, but deferred ordering a recount until the case was better developed.

"I must say Mr Solicitor-General, looking at the material last night, I thought it was a little light on," he said.

Ms Kakoschke-Moore's lawyer David Jackson told the court she had now renounced her British citizenship, and wanted to be part of a recount.

Mr Jackson pointed out that the likely replacement, Tim Storer was no longer a member of the party, and would not reflect the choice exercised by the voters.

Justice Nettle said that could be a problem for Ms Kakoschke-Moore in view of the recent decision which ruled out Hollie Hughes as the replacement for former senator Fiona Nash.

"This lady was disqualified in the time after the election," he said.

But Mr Jackson said he wanted to argue to the contrary, knowing it may drag out the process.

"I suspect Your Honour this is a matter for which all members of the court will have to sit at some point," he said.

Mr Donaghue urged the court not to delay beyond early February when the Senate resumes.

"There's a public interest in having it resolved by then," he said.

The case will be back for directions in January.