Mind missing British weather (4)
I believe the answer is:
rain
'weather' is the definition.
(rain is a kind of weather)
'mind missing british' is the wordplay.
'mind' becomes 'brain' ('brain' can be a synonym of 'mind').
'missing' indicates named letters should be taken away.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'brain' with 'b' removed is 'RAIN'.
(Other definitions for rain that I've seen before include "Falling moisture" , "Fall wetly" , "Cats and dogs?" , "Fall in large quantities" , "Wet weather" .)