Complained peevishly, upsetting me, my dear! (8)
I believe the answer is:
yammered
'complained peevishly' is the definition.
(yammer can mean to complain about something)
'upsetting me my dear' is the wordplay.
'upsetting' is an anagram indicator.
'me'+'my'+'dear'='memydear'
'memydear' anagrammed gives 'YAMMERED'.
(Other definitions for yammered that I've seen before include "Made a loud and incessant noise" , "Complained" , "having made an outcry" .)