The most common and most likely answer to this crossword clue is the 8 letter word ANGRIEST
I've seen this crossword clue in The Daily Telegraph
A
N
G
R
I
E
S
T
More clues leading to the result ANGRIEST
- Great sin could make you most irate
- Fear fencing that is on river most cross
- Degradation of inert gas, most furious
- Most irritated rook that is in distress
- Most resentful, driven to extremes by Anglican priest
- Extremely mad king that is beset by dread
- Most passionate redhead that’s in distress
- Granite’s broken, extremely cross
- Inert gas making one extremely cross
- Resign at work, becoming most irritated
Buddy explains!

The straight part
We know that "most incensed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most incensed = angriest.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ANGRIEST mean?
ANGRIEST adjective- Displaying or feeling anger.
- (said about a wound or a rash) Inflamed and painful.
- (said about the elements, like the sky or the sea) Dark and stormy, menacing.