Extremely rude bore that may be infuriating (3,3)
I believe the answer is:
red rag
'that may be infuriating' is the definition.
(as in a red rag to a bull)
'extremely rude bore' is the wordplay.
'extremely' says to hollow out the word (remove centre letters) (only the extremes of the word are used).
'bore' becomes 'drag' (I've seen this in another clue).
'rude' with its middle taken out is 're'.
're'+'drag'='RED RAG'
(Other definitions for red rag that I've seen before include "Provocation to bull" , "Source of extreme provocation" , "Gerard (anag) - cause of infuriation" , "Reputed to annoy bull" , "Something proverbially annoying a bull" .)