Year in Latin and year in Greek, originally exasperating (8)
I believe the answer is:
annoying
'exasperating' is the definition.
(synonyms)
'year in latin and year in greek originally' is the wordplay.
'year in latin' becomes 'anno' (I've seen this in another clue).
'and' means one lot of letters go next to another.
'year' becomes 'y'.
'originally' suggests taking the first letters.
The first letter of 'greek' is 'g'.
'anno'+'y'+'in'+'g'='ANNOYING'
(Other definitions for annoying that I've seen before include "Disturbing, irritating" , "Irksome" , "Vexing" , "Irritating, bothersome" , "Vexatious" .)