Line travelled by river (4)
I believe the answer is:
nile
'river' is the definition.
(I know that Nile is a river)
'line travelled' is the wordplay.
'travelled' is an anagram indicator.
'line' anagrammed gives 'NILE'.
'by' is the link.
(Other definitions for nile that I've seen before include "Take a line to the river" , "Egypt's river" , "Long river" , "Cleopatra's river" , "Line (anag)" .)