Quietly optimistic about start of peace he forecast (8)
I believe the answer is:
prophesy
'forecast' is the definition.
(prophesying is a kind of forecasting)
'quietly optimistic about start of peace he' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'optimistic' becomes 'rosy' ('rosy' can be similar in meaning to 'optimistic').
'about' is an insertion indicator.
'start of' suggests taking the first letters.
The initial letter of 'peace' is 'p'.
'p'+'he'='phe'
'rosy' going around 'phe' is 'rophesy'.
'p'+'rophesy'='PROPHESY'
(Other definitions for prophesy that I've seen before include "Foretell - portend" , "Say that something will happen in the future" , "Predict" , "Prediction" , "Reveal through divine inspiration" .)