Bright, though with bad weather coming through next (6)
I believe the answer is:
brainy
'bright' is the definition.
(both can mean intelligent)
'with bad weather coming through next' is the wordplay.
I cannot quite see how this works, but
'weather' could be 'rain' (rain is a kind of weather) and 'rain' is found within the answer.
'with' could be 'by' (both can mean close together) and 'by' is located in the remaining letters.
This accounts for all the letters.
This explanation may well be incorrect...
'though' is the link.
Can you help me to learn more?
(Other definitions for brainy that I've seen before include "Clever, got lots of grey matter" , "Bright" , "Having a high IQ" , "Binary (anag.)" , "Intellectual" .)