Undermine part of the rodeo (5)
I believe the answer is:
erode
'undermine' is the definition.
(I've seen this in another clue)
'part of the rodeo' is the wordplay.
'part of' indicates a hidden word.
'ERODE' is hidden in the letters of 'the rodeo'.
(Other definitions for erode that I've seen before include "go to pieces!" , "Gradually wear away" , "Corrode" , "Wear away with weather" , "'Deteriorate, wear away (5)'" .)