Travel, moving out to the right (4)
I believe the answer is:
tour
'travel' is the definition.
(touring is a kind of travelling)
'moving out to the right' is the wordplay.
'moving' is an anagram indicator.
'to the right' becomes 'r' (common abbreviation).
'out' anagrammed gives 'tou'.
'tou'+'r'='TOUR'
(Other definitions for tour that I've seen before include "Journey with frequent stops" , "... de France is a multi-stage cycle race" , "Journey around" , "Journey visiting several different places" , "Extended journey" .)