British prince getting smarter (8)
I believe the answer is:
brainier
'smarter' is the definition.
(I've seen this before)
'british prince getting' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'prince' becomes 'rainier' (Prince Rainier of Monaco).
'getting' is a charade indicator (letters next to each other).
'b'+'rainier'='BRAINIER'
(Other definitions for brainier that I've seen before include "appearing brighter" , "more clever!" , "smarter" , "With a higher IQ?" , "More intelligent (colloq.)" .)