Drama teacher’s outmoded form of transport (10)
I believe the answer is:
stagecoach
'transport' is the definition.
(stagecoach is a kind of transport)
'drama teacher's outmoded form' is the wordplay.
I cannot quite understand how this works, but
'form' could be 'stage' (I have seen 'Form of transport' mean 'stage' so perhaps 'form' could also mean 'stage') and 'stage' is found within the answer.
'teacher' could be 'coach' (coach is a kind of teacher) and 'coach' is found within the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'of' acts as a link.
Can you help me to learn more?
(Other definitions for stagecoach that I've seen before include "John Wayne film; passenger vehicle" , "One gets around stops" , "Travelling" , "Great Western" , "Picture of Ford's" .)