Travelled on right lines (4)
I believe the answer is:
rode
'travelled' is the definition.
(eg travelled on a horse)
'on right lines' is the wordplay.
'on' says to put letters next to each other.
'right' becomes 'r' (common abbreviation).
'lines' becomes 'ode' (lines of poetry).
'r' put next to 'ode' is 'RODE'.
(Other definitions for rode that I've seen before include "Travelled by bike" , "Went by horse" , "Went on horeseback" , "Went mounted" , "Travelled on horse" .)