Run through former play by Goethe, hard for following (7)
I believe the answer is:
exhaust
'run through' is the definition.
('exhaust' can be a synonym of 'run through')
'former play by goethe hard for following' is the wordplay.
I cannot quite see how this works, but
'former' could be 'ex' and 'ex' is located in the answer.
'hard' could be 'h' and 'h' is located in the answer.
This explanation may well be incorrect...
(Other definitions for exhaust that I've seen before include "part of car - > tire?" , "Deplete" , "Weary" , "Completely tire out" , "Car's waste gas" .)