Clarke is sidelined amid reports that a long-standing back injury flared up after Australia's crushing second Test defeat against England at Lord's.
Ed Cowan will skipper the team in Clarke's absence, with vice-captain Brad Haddin, openers Shane Watson and Chris Rogers plus pace bowlers Peter Siddle and Ryan Harris all rested.
Those changes mean a surprise chance for Turner, who had been playing in the English amateur leagues for Chichester Priory Park as part of a development programme run by Cricket Australia and Hampshire.
Turner, a member of the Australia Under-19 team that finished runners-up to India in last year's World Cup, was one of six Australian Institute Of Sport scholars to be awarded a summer placement in England.
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His call-up means Australia will field three spinners against Sussex as Ashton Agar and Nathan Lyon were already included.
With Australia in crisis after falling 2-0 behind in the five-Test series, their hopes of regaining the Ashes suffered a further blow on Monday when pace bowler James Pattinson was ruled out for the rest of the series with a stress fracture of his lower back.