Irritation of King George, trapped by succession (7)
I believe the answer is:
chagrin
'irritation' is the definition.
'king george trapped by succession' is the wordplay.
'king george' becomes 'gr' (Georgius Rex).
'trapped by' is an insertion indicator.
'succession' becomes 'chain' (I've seen this before).
'gr' going within 'chain' is 'CHAGRIN'.
'of' acts as a link.
(Other definitions for chagrin that I've seen before include "irritation?" , "Embarrassment - rich nag (anag)" , "Arching with annoyance and embarrassment" , "anything but delight" , "Acute annoyance or disappointment" .)