Investigator actually overlooking it, causing annoyance (5)
I believe the answer is:
pique
'annoyance' is the definition.
(I know that pique is a type of annoyance)
'investigator actually overlooking it' is the wordplay.
'investigator' becomes 'pi' (I've seen this in other clues).
'actually overlooking' becomes 'qu' (I can't justify this - if you can you should give a lot more credence to this answer).
'it' becomes 'e' ('e' can mean 'electronic' which is similar to 'IT').
'pi'+'qu'+'e'='PIQUE'
'causing' acts as a link.
Can you help me to learn more?
(Other definitions for pique that I've seen before include "A feeling of hurt pride" , "Resentful feeling" , "Resentment; hurt pride" , "Nettle" , "Dudgeon" .)