Travel free heading for Eastbourne (4)
I believe the answer is:
ride
'travel' is the definition.
(riding is a kind of travelling)
'free heading for eastbourne' is the wordplay.
'free' becomes 'rid' ('rid' can be a synonym of 'free'**).
'heading for' suggests taking the first letters.
The first letter of 'eastbourne' is 'e'.
'rid'+'e'='RIDE'
(Other definitions for ride that I've seen before include "Travel by horse, bus, etc" , "Travel upon" , "Fairground entertainment" , "Journey as passenger" , "Fairground attraction; go on horseback" .)