Travelling on her river (5)
I believe the answer is:
rhone
'river' is the definition.
(Rhone River is an example)
'travelling on her' is the wordplay.
'travelling' indicates anagramming the letters.
'on'+'her'='onher'
'onher' is an anagram of 'RHONE'.
(Other definitions for rhone that I've seen before include "European river and glacier" , "Camargue river" , "River running through the city of Arles" , "wherein runs rain in Arbroath" , "River flowing through Lake Geneva" .)