Annoys with very quiet wavelets (7)
I believe the answer is:
ripples
'wavelets' is the definition.
('ripple' can be a synonym of 'wavelet')
'annoys with very quiet' is the wordplay.
'annoys' becomes 'riles' ('rile' can be a synonym of 'annoy').
'with' indicates putting letters inside.
'very quiet' becomes 'pp'.
'riles' going around 'pp' is 'RIPPLES'.
(Other definitions for ripples that I've seen before include "Small waves around slipper" , "Wavelets" .)