European staff started old cowboy contest (5)
I believe the answer is:
rodeo
'cowboy contest' is the definition.
(I've seen this in another clue)
'european staff started old' is the wordplay.
'european' becomes 'E' (abbreviation e.g. EU).
'staff' becomes 'rod' (both can mean a stick or cane).
'started' is a charade indicator (letters next to each other).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'e' put after 'rod' is 'rode'.
'rode'+'o'='RODEO'
(Other definitions for rodeo that I've seen before include "One should be up for this event" , "display of cowboy skill" , "Drive in Beverly Hills" , "American show" , "Cattle round-up" .)