Blustery at first with more showers, becoming brighter (8)
I believe the answer is:
brainier
'brighter' is the definition.
(bright can mean brainy or clever)
'blustery at first with more showers' is the wordplay.
'at first' says to take the initial letters.
'with more showers' becomes 'rainier' (rain showers).
The first letter of 'blustery' is 'b'.
'b'+'rainier'='BRAINIER'
'becoming' acts as a link.
(Other definitions for brainier that I've seen before include "More intelligent (colloq.)" , "more clever!" , "With a higher IQ?" , "appearing brighter" , "smarter" .)