Annoying hack working, missing nothing (7)
I believe the answer is:
nagging
'annoying' is the definition.
(nag can mean to annoy or badger)
'hack working missing nothing' is the wordplay.
'hack' becomes 'nag' (synonyms).
'working' becomes 'going' (working can mean going or activated).
'missing' indicates named letters should be taken away.
'nothing' becomes 'O' (O resembles 0).
'going' with 'o' removed is 'ging'.
'nag'+'ging'='NAGGING'
(Other definitions for nagging that I've seen before include "Pestering, plaguing" , "Persistently worrying" , "Continually complaining or faultfinding" , "Carping" , "Complaining continuously" .)