Show runs rings around disheartened debutante (5)
I believe the answer is:
rodeo
'show' is the definition.
(rodeo is a kind of show)
'runs rings around disheartened debutante' is the wordplay.
'runs' becomes 'r' (cricket abbreviation**).
'rings' becomes 'oo' (multiple circles).
'around' is an insertion indicator.
'disheartened' means to remove the middle letters.
'debutante' with its middle removed is 'de'.
'oo' going around 'de' is 'odeo'.
'r'+'odeo'='RODEO'
(Other definitions for rodeo that I've seen before include "display of cowboy skill" , "Cowboy riding contest" , "Contest of cowboy skills" , "Horse sporting event for cowboys" , "stock venue?" .)