Ultimately successful climber, a chronicler of Roman history (4)
I believe the answer is:
livy
'a chronicler of roman history' is the definition.
(Roman historian)
'ultimately successful climber' is the wordplay.
'ultimately' suggests the final letters.
'climber' becomes 'ivy' (ivy is a climbing plant).
The last letter of 'successful' is 'l'.
'l'+'ivy'='LIVY'
(Other definitions for livy that I've seen before include "Roman historian" , "Poet" .)