Letter governor sent in to Times needing answer (5)
I believe the answer is:
theta
'letter' is the definition.
(Greek letter)
'governor sent in to times needing answer' is the wordplay.
'governor' becomes 'HE' (His or Her Excellency, address for a governor).
'sent in' is an insertion indicator.
'to times' becomes 'tt' (an abbreviation for time written twice).
'needing' is a charade indicator (letters next to each other).
'answer' becomes 'a' (abbreviation eg in Q and A).
'he' going into 'tt' is 'thet'.
'thet'+'a'='THETA'
(Other definitions for theta that I've seen before include "letter from abroad" , "Letter from Greece" , "Letter to the Corinthians" , "Greek character" , "Eighth letter of Greek alphabet" .)