South Australian Premier Steven Marshall has unveiled his new-look cabinet, following the resignations of three senior ministers on Sunday over the state's expenses scandal.

The Speaker of the Lower House, Vincent Tarzia, as well as backbenchers David Basham and Stephen Patterson will gain ministerial roles.

Mr Tarzia will take over the police portfolio, Mr Basham will look after agriculture and Mr Patterson will handle trade and investment.

Deputy Premier Vickie Chapman will add planning and local government to her roles, while Corey Wingard will add infrastructure and transport to his sport, recreation and racing portfolios.

Resignations over allowance claims

The saga began when an ABC investigation raised serious questions over the eligibility of former Legislative Council president Terry Stephens to claim an accommodation allowance for country MPs.

Several Liberal MPs have since volunteered to repay tens of thousands of dollars claimed under the travel allowance.

Ministers Stephan Knoll and Tim Whetstone resigned on Sunday after it was revealed they had claimed Country Members Accommodation Allowances before incurring any costs.

They also claimed the allowance while not in Adelaide.

David Ridgway admitted signing blank time sheets for his chauffeur while the minister was away on an overseas holiday.

"I would like to very much thank all of the outgoing ministers from our Cabinet for their exceptional work in the Cabinet — the work they did to help us transition into Government," Mr Marshall said.

No new women in Cabinet

Marginal southern suburbs MP Carolyn Power had been tipped to rise to Cabinet but missed out.

"There were many, many people we considered," Mr Marshall said.

"I've got to say we are spoilt for choice in the Liberal party room at the moment, but I've formed the opinion that this provides the best balance, the best fit for the portfolios that were available."

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The new Cabinet only has two Upper House members — down from three — with Treasurer Rob Lucas hanging onto his role despite planning to retire at the 2022 state election.

A swearing-in ceremony will be held on Wednesday morning ahead of the first new Cabinet meeting on Thursday.

There will be no speaker while Parliament is in recess, Mr Marshall said.

"I don't think it will pose us any problems whatsoever," he said.

A replacement will also need to be found for Mr Stephens as Legislative Council president.

Mr Stephens quit despite not admitting any fault in claiming the Country Members Accommodation Allowance while spending much of his time in the inner Adelaide suburb of Norwood.