Old transport for a drama teacher? (5-5)

I believe the answer is:

stage-coach

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

'old transport for a drama' is the wordplay.
'old transport' becomes 'stage' (I've seen this in another clue).
'for' says to put letters next to each other.
'a drama' becomes 'coach' (I can't explain this - if you can you should believe this answer much more).
'stage'+'coach'='STAGE-COACH'

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

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