Former public vehicle for theatre instructor (5,5)

I believe the answer is:

stage coach

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'former public vehicle' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'theatre instructor' is the wordplay.
'theatre' becomes 'stage' (stage is a kind of theatre).
'instructor' becomes 'coach' (coach is a kind of instructor).
'stage'+'coach'='STAGE-COACH'

'for' is the link.

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I've seen this clue in the Sydney Morning Herald.

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