Went on the right lines (4)
I believe the answer is:
rode
'went on' is the definition.
(I've seen this in another clue)
'right lines' is the wordplay.
'right' becomes 'r' (common abbreviation).
'lines' becomes 'ode' (I've seen this before).
'r'+'ode'='RODE'
'the' is the link.
(Other definitions for rode that I've seen before include "Went mounted" , "Went on horseback" , "Went by horse" , "did some travelling" , "Travelled on the back of an animal" .)