Annoyance at smile after tea (7)
I believe the answer is:
chagrin
'annoyance' is the definition.
(I've seen this before)
'smile after tea' is the wordplay.
'smile' becomes 'grin' (grinning is a kind of smiling).
'after' means one lot of letters go next to another.
'tea' becomes 'cha' (cha is a type of tea).
'grin' after 'cha' is 'CHAGRIN'.
'at' is the link.
(Other definitions for chagrin that I've seen before include "Feeling of annoyance and embarrassment" , "Discomfiture" , "irritation?" , "Arching with annoyance and embarrassment" , "Emotion" .)