Feature filled with anger regularly reveals annoyance (7)
I believe the answer is:
chagrin
'annoyance' is the definition.
(I've seen this before)
'feature filled with anger regularly' is the wordplay.
'feature' becomes 'chin' (facial feature).
'filled with' indicates putting letters inside.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternating letters of 'anger' are 'agr'.
'chin' placed around 'agr' is 'CHAGRIN'.
'reveals' acts as a link.
(Other definitions for chagrin that I've seen before include "Discomfiture" , "Acute annoyance or disappointment" , "Arching with annoyed disappointment" , "Shame at having failed" , "Embarrassment - rich nag (anag)" .)