Travelled on horseback finally to cattle round-up (5)
I believe the answer is:
rodeo
'cattle round-up' is the definition.
(I've seen this before)
'travelled on horseback finally to' is the wordplay.
'travelled on horseback' becomes 'rode'.
'finally' suggests the final letters.
The last letter of 'to' is 'o'.
'rode'+'o'='RODEO'
(Other definitions for rodeo that I've seen before include "At which cowboys show their skills" , "Exhibition of cowboy skills" , "A bunch of cowboys, showing" , "off, sometimes" , "Wild West show" .)