Annoyed at getting into rage (5)
I believe the answer is:
irate
'annoyed' is the definition.
(I've seen this before)
'at getting into rage' is the wordplay.
'getting into' is an insertion indicator.
'rage' becomes 'ire' (I've seen this before).
'at' placed within 'ire' is 'IRATE'.
(Other definitions for irate that I've seen before include "ranting" , "will be up in arms" , "Extremely cross" , "Not happy" , "Livid" .)