To annoy persistently is mean! (3,2)
I believe the answer is:
get at
This clue is a double definition.
'to annoy persistently' is the first definition.
'mean' is the second definition.
(as in what a speaker means or is 'getting at')
'is' is the link.
(Other definitions for get at that I've seen before include "Reach - mean - attack verbally" , "Criticise (someone)" , "Intend" , "Nobble; gain access to" , "Pick on - gain access to" .)