Cheers! Australia's booted out tech giant (5)
I believe the answer is:
apple
'tech giant' is the definition.
(Apple is a technology company)
'cheers australia's booted out' is the wordplay.
'cheers' becomes 'applause' (cheers from an audience).
'australia's' becomes 'au's'.
'booted out' is a deletion indicator.
'applause' with 'aus' taken away is 'APPLE'.
(Other definitions for apple that I've seen before include "award from Paris" , "Eve's fruit" , "Beneficiary of 23 [LOVELACE]" , "One poisoned Disney's Snow White" , "Pome fruit" .)