I grew annoyed about a little pest (6)
I believe the answer is:
earwig
'little pest' is the definition.
Although both the answer and definition are singular nouns, I cannot see how one could define the other.
'i grew annoyed about a' is the wordplay.
'annoyed' is an anagram indicator.
'about' means one lot of letters goes inside another.
'i'+'grew'='igrew'
'igrew' with letters rearranged gives 'erwig'.
'erwig' placed around 'a' is 'EARWIG'.
Can you help me to learn more?
(Other definitions for earwig that I've seen before include "listen in?" , "Eavesdrop (informal)" , "flatterer" , "An insect, I wager (anag.)" , "Small insect with pincers at end of its body" .)