Going away, transported by vile nag (7)
I believe the answer is:
leaving
'going away' is the definition.
(synonyms)
'transported by vile nag' is the wordplay.
'transported' indicates anagramming the letters.
'by' says to put letters next to each other.
'vile' after 'nag' is 'nagvile'.
'nagvile' is an anagram of 'LEAVING'.
(Other definitions for leaving that I've seen before include "Going away" , "Abandoning" , "Bequeathing (in will)" , "Departing" , "Departure" .)