Secret Service after prince over Virginia (7)
I believe the answer is:
private
'secret' is the definition.
(I know that secret can be written as private)
'service after prince over virginia' is the wordplay.
'service' becomes 'rite' (a religious service).
'after' means one lot of letters go next to another.
'prince' becomes 'p' (abbreviation).
'over' indicates putting letters inside.
'virginia' becomes 'va' (US state abbreviation).
'rite' after 'p' is 'prite'.
'prite' placed around 'va' is 'PRIVATE'.
(Other definitions for private that I've seen before include "One's own" , "Arm y rank" , "To most, unknown" , "Secret sort of soldier" , "Secret - soldier of the lowest rank" .)