She removed the senior figures who had backed her rival in the Tory leadership race promptly after heading to her House of Commons office following her first speech in Downing Street on Tuesday.
Mr Raab, who was justice secretary as well as second in command to Boris Johnson, had not expected to continue his run in government, having described Ms Truss’s tax plans as an "electoral suicide note".
Other ministers to leave the frontbench on Tuesday include Andrew Stephenson, the Conservative party chairman, Johnny Mercer, the veterans affairs minister, and Greg Clark, the levelling up secretary.
Northern Ireland Secretary Shailesh Vara and Environment Secretary George Eustice have also been sacked.
On Monday, Priti Patel and Nadine Dorries both left office, despite neither endorsing Mr Sunak in the leadership race.
Another Johnson ally, Ben Elliot, also stepped back as Conservative Party co-chairman following Ms Truss’s victory.
Ms Dorries told ITV News Reporter Daniel Hewitt she was offered to stay on as culture secretary by Ms Truss but "after a lot of soul searching" she has declined.
She also refused to answer whether she's standing down as an MP.
Mr Raab said he would be supporting the government from the backbenches and wished Ms Truss good luck.
Mr Shapps also tweeted his own exit as Transport Secretary but did not make the same remarks of support for the new Tory leader.
“It has been a privilege to serve as Transport Secretary; a job I loved,” he said.
“Now I look forward to being a strong, independent voice on the backbenches, developing policies that will further the Conservative cause and the interests of my constituents in Welwyn Hatfield.”
Mr Barclay, the MP for North East Cambridgeshire who had been health secretary for Mr Johnson’s final months in office, tweeted: “Thanks to all colleagues, both political & civil service, for their fantastic support. Wishing @trussliz & her ministerial team every success for the future.”
Mr Sunak, the former chancellor whose resignation helped trigger the downfall of Boris Johnson, has also made clear he does not expect to be offered a new job.
His supporters, however, have been urging Ms Truss to appoint an “inclusive” Cabinet and not simply surround herself with loyalists in the way that Mr Johnson was accused of doing.
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