The most common and most likely answer to this crossword clue is the 4 letter word BILE
I've seen this crossword clue in The Daily Telegraph
B
I
L
E
More clues leading to the result BILE
Buddy explains!

The straight part
We know that "anger" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case anger = bile.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 BILE mean?
BILE noun- A bitter brownish-yellow or greenish-yellow secretion produced by the liver, stored in the gall bladder, and discharged into the duodenum where it aids the process of digestion.
- Bitterness of temper; ill humour; irascibility.
- Two of the four humours, black bile or yellow bile, in ancient and medieval physiology.
- A boil (kind of swelling).
- (of liquids) To heat to the point where it begins to turn into a gas.
- To cook in boiling water.
- (of liquids) To begin to turn into a gas, seethe.
- To bring to a boil, to heat so as to cause the contents to boil.
- (used only in progressive tenses, of weather) To be uncomfortably hot.
- (used only in progressive tenses) To feel uncomfortably hot.
- To form, or separate, by boiling or evaporation.
- To steep or soak in warm water.
- To be agitated like boiling water; to bubble; to effervesce.
- To be moved or excited with passion; to be hot or fervid.