Girl beginning to annoy Virginia (3)
I believe the answer is:
ava
'girl' is the definition.
'beginning to annoy virginia' is the wordplay.
'beginning to' indicates taking the first letters.
'virginia' becomes 'va' (US state abbreviation).
The initial letter of 'annoy' is 'a'.
'a'+'va'='AVA'
(Other definitions for ava that I've seen before include "woman" , "girl" , ". . . Gardner (film star)" , "- - Gardner (films)" , "-- Gardner, US actress" .)