Peer announced or articulated crown's annoyance (5)
I believe the answer is:
pique
'articulated crown's annoyance' is the definition.
'pique' can be an answer for 'annoyance' (pique is a kind of annoyance). I'm unsure of the 'articulated crown's' bit.
'peer announced' is the wordplay.
'peer' becomes 'peek'.
'announced' indicates a 'sounds like' (homophone) clue.
'peek' sounds like 'PIQUE'.
'or' acts as a link.
Can you help me to learn more?
(Other definitions for pique that I've seen before include "A feeling of hurt pride" , "Animosity" , "Dudgeon" , "Resentful feeling" , "Arouse" .)