Ancient Greek starts to annoy everyone spouting old parables (5)
I believe the answer is:
aesop
'ancient greek' is the definition.
'Aesop' can be an answer for 'greek' (Aesop is an example). I am not certain of the 'ancient' bit.
'starts to annoy everyone spouting old parables' is the wordplay.
'starts to' indicates taking the first letters.
The first letters of 'annoy everyone spouting old parables' is 'AESOP'.
Can you help me to learn more?
(Other definitions for aesop that I've seen before include "Greek father of fables" , "story teller" , "Fable-teller" , "Greek storyteller" , "Greek fable writer" .)