Was up on bronco's back in Wild West Show (5)
I believe the answer is:
rodeo
'wild west show' is the definition.
(I've seen this before)
'was up on bronco's back' is the wordplay.
'was up' becomes 'rode' (I've seen this in other clues).
'on' says to put letters next to each other.
'back' says to take the final letters.
The last letter of 'bronco' is 'o'.
'rode'+'o'='RODEO'
'in' is the link.
(Other definitions for rodeo that I've seen before include "One should be up for this event" , "competition in cowboy skills" , "American show" , "sort of exhibition" , "Cattle round-up" .)