After tea, smile at the annoyance! (7)
I believe the answer is:
chagrin
'the annoyance' is the definition.
(I've seen this before)
'after tea smile' is the wordplay.
'after' is a charade indicator (letters next to each other).
'tea' becomes 'cha' (cha is a type of tea).
'smile' becomes 'grin' (grinning is a kind of smiling).
'cha'+'grin' is 'CHAGRIN'.
'at' acts as a link.
(Other definitions for chagrin that I've seen before include "Feeling of vexation or embarrassment" , "Feeling of annoyance and embarrassment" , "Disappointment, exasperation" , "Strong feeling of embarrassment" , "Annoy" .)