Sweetheart's after free travel (4)
I believe the answer is:
ride
'travel' is the definition.
(riding is a kind of travelling)
'sweetheart's after free' is the wordplay.
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'after' says to put letters next to each other.
'free' becomes 'rid' ('rid' can be a synonym of 'free'**).
'e' put after 'rid' is 'RIDE'.
(Other definitions for ride that I've seen before include "Journey on horse?" , "Travel by horse, bus, etc" , "Sit on (a horse/vehicle)" , "Fairground attraction; go on horseback" , "Journey on horseback" .)