Progressive crossbenchers say they have lost trust in the Tasmanian government over the terms of reference for a promised study into the state's salmon industry.

But the issue appears unlikely to result in another no-confidence vote in Premier Jeremy Rockliff, who remained in power after the snap state election in July — Tasmania's fourth election in seven years.

Mr Rockliff promised the study on August 17 while in discussions with crossbenchers after the election, which delivered a near-identical parliament, with one of the changes being the addition of anti-salmon farming independent Peter George.

To eat or not to eat? The fight over Tasmanian salmon

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The terms of reference for the independent

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