Forecaster is upset over Times letters initially (5)
I believe the answer is:
sibyl
'forecaster' is the definition.
(sibyl is a kind of forecaster)
'is upset over times letters initially' is the wordplay.
'upset' says the letters should be written in reverse.
'over' is a charade indicator (letters next to each other).
'times' becomes 'by' (both can mean 'multiplied by').
'initially' suggests taking the first letters.
The initial letter of 'letters' is 'l'.
'is' reversed gives 'si'.
'si'+'by'+'l'='SIBYL'
(Other definitions for sibyl that I've seen before include "Ancient seer - prophetess" , "Greek oracle" , "Woman mouthpiece of a god, uttering prophecies" , "Female seer" , "prophet" .)