Annoyed about one insect in pastry (9)
I believe the answer is:
croissant
'pastry' is the definition.
(I have seen 'French pastry ' mean 'croissant' so perhaps 'pastry' could also mean 'croissant')
'annoyed about one insect in' is the wordplay.
'annoyed' becomes 'cross' (I've seen this before).
'about' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'insect in' becomes 'ant' (I can't explain this - if you can you should believe this answer much more).
'cross' enclosing 'i' is 'croiss'.
'croiss'+'ant'='CROISSANT'
(Other definitions for croissant that I've seen before include "French breakfast food" , "food item" , "French pastry" , "Breakfast pastry" , "Bread-roll" .)