I leave right after a Russian (4)
I believe the answer is:
igor
'a russian' is the definition.
(common Russian name)
'i leave right' is the wordplay.
'leave' becomes 'go' (to go is to depart or leave).
'right' becomes 'r' (common abbreviation).
'i'+'go'+'r'='IGOR'
'after' is the link.
(Other definitions for igor that I've seen before include "Russian boy" , "Stravinsky's first name" , "Prince in Borodin's opera" , "Stravinsky, for example" , "Prince --, opera by Borodin" .)