Quiet formal announcement following end of weather forecast (7)
I believe the answer is:
predict
'forecast' is the definition.
(synonyms)
'quiet formal announcement following end of weather' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'formal announcement' becomes 'edict' (I've seen this before).
'following' is a charade indicator (letters next to each other).
'end of' suggests the final letters.
The final letter of 'weather' is 'r'.
'edict' after 'r' is 'redict'.
'p'+'redict'='PREDICT'
(Other definitions for predict that I've seen before include "Divine" , "Anticipate" , "Foresee" , "Estimate consequence of" , "act as oracle" .)