Classic venue where doctor’s exercising back (5)
I believe the answer is:
epsom
'classic venue' is the definition.
(venue for one of the Classic British horse races)
'doctor's exercising back' is the wordplay.
'doctor's' becomes 'mo's' (medical officer).
'exercising' becomes 'pe' (abbreviation for Physical Education).
'back' says the letters should be written backwards.
'mos'+'pe'='mospe'
'mospe' in reverse letter order is 'EPSOM'.
'where' acts as a link.
(Other definitions for epsom that I've seen before include "Poems about the race-course" , "Classic racecourse" , "can have horses" , "Derby and Oaks racecourse" , "Home to the Derby and the Oaks" .)