Noisily rise, being peeved (4)
I believe the answer is:
sore
'peeved' is the definition.
(I've seen this in another clue)
'noisily rise' is the wordplay.
'noisily' shows a homophone (sound like).
'rise' becomes 'soar' (soaring is a kind of rising).
'soar' sounds like 'SORE'.
'being' is the link.
(Other definitions for sore that I've seen before include "Eros (anag.)" , "See 16" , "Hurtful to the touch, like rose" , "Aggrieved" , "Painful spot" .)