Snap after Prince's angry words (9)
I believe the answer is:
philippic
'angry words' is the definition.
(a philippic is a bitter or angry speech)
'snap after prince's' is the wordplay.
'snap' becomes 'pic' (short for picture).
'after' means one lot of letters go next to another.
'prince' becomes 'Philip' (Prince Philip, the Duke of Edinburgh).
'pic' put after 'philip' is 'PHILIPPIC'.
(Other definitions for philippic that I've seen before include "angry speech" , "Speech denouncing" , "King of Spain" , "Verbal attack" , "Denunciatory speech" .)