Drove to see old show (5)
I believe the answer is:
rodeo
'show' is the definition.
(I know that rodeo is a type of exhibition)
'drove to see old' is the wordplay.
'drove' becomes 'rode' (ride can mean to travel by car).
'to see old' becomes 'o' (abbreviation).
'rode'+'o'='RODEO'
(Other definitions for rodeo that I've seen before include "Wild West contest" , "A bunch of cowboys, showing" , "off, sometimes" , "show with mounting excitement" , "Show with broncobusters" .)