Nag's comment beginning to bother the Guardian's local resident (9)
I believe the answer is:
neighbour
'local resident' is the definition.
(someone who lives in the neighbourhood)
'nag's comment beginning to bother the guardian's' is the wordplay.
'nag's comment' becomes 'neigh' (sound made by a horse).
'beginning to' indicates taking the first letters.
'the guardian's' becomes 'our' (belonging to the newspaper the puzzle appears in).
The first letter of 'bother' is 'b'.
'neigh'+'b'+'our'='NEIGHBOUR'
(Other definitions for neighbour that I've seen before include "someone close" , "Chap next door" , "Person alongside" , "One lives nearby" , "one located nearby" .)