Accompany a coster on the move (6)
I believe the answer is:
escort
'accompany' is the definition.
(I know that escort is a more specific form of the action accompany)
'a coster on the move' is the wordplay.
'on the move' indicates anagramming the letters.
'coster' anagrammed gives 'ESCORT'.
(Other definitions for escort that I've seen before include "conduct" , "Provide company - car - guard" , "wheels?" , "Entourage" , "Act as companion, attend" .)