Fido's annoyance (4)
I believe the answer is:
flea
'fido's annoyance' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for flea that I've seen before include "Irritating jumper?" , "Bloodsucking parasite" , "Tiny parasite" , "beastie?" , "Small jumper in small circus" .)