Greek breaking shackles displays annoyance (7)
I believe the answer is:
chagrin
'annoyance' is the definition.
(I've seen this before)
'greek breaking shackles' is the wordplay.
'greek' becomes 'gr' (abbreviation for Greek).
'breaking' indicates putting letters inside.
'shackles' becomes 'chain'.
'gr' inserted inside 'chain' is 'CHAGRIN'.
'displays' acts as a link.
(Other definitions for chagrin that I've seen before include "Embarrassment - rich nag (anag)" , "Annoyance/shame at one's failure" , "irritation?" , "Arching with annoyed disappointment" , "Humiliation, mortification" .)