Cycled to old show (5)
I believe the answer is:
rodeo
'show' is the definition.
(rodeo is a kind of show)
'cycled to old' is the wordplay.
'cycled' becomes 'rode' (I've seen this before).
'to old' becomes 'o' (common abbreviation eg in OE for Old English).
'rode'+'o'='RODEO'
(Other definitions for rodeo that I've seen before include "display of cowboy skill" , "Show with broncobusters" , "Horse-riding competition for cowboys" , "Cowboy event" , "stock venue?" .)