I depart right after the operatic prince (4)
I believe the answer is:
igor
'the operatic prince' is the definition.
(subject of Borodin opera)
'i depart right' is the wordplay.
'depart' becomes 'go' (synonyms).
'right' becomes 'r' (common abbreviation).
'i'+'go'+'r'='IGOR'
'after' acts as a link.
(Other definitions for igor that I've seen before include "Prince in Borodin's opera" , "-- Stravinsky, composer" , "Stravinsky, perhaps" , "Hero of Borodin" , "Prince of Russian opera" .)