Annoyance with broad smile after brief chat (7)
I believe the answer is:
chagrin
'annoyance' is the definition.
(I've seen this before)
'broad smile after brief chat' is the wordplay.
'broad smile' becomes 'grin' (I've seen this before).
'after' is a charade indicator (letters next to each other).
'brief' means to remove the last letter (a shorter or briefer version of the word).
'chat' with its last letter taken off is 'cha'.
'grin' after 'cha' is 'CHAGRIN'.
'with' is the link.
(Other definitions for chagrin that I've seen before include "Feeling of annoyance and embarrassment" , "Discomfiture" , "Frustration at having failed" , "Strong feeling of embarrassment" , "anything but delight" .)