The most common and most likely answer to this crossword clue is the 6 letter word ANGERS
I've seen this crossword clue in The Daily Telegraph
A
N
G
E
R
S
More clues leading to the result ANGERS
- Beat-up cars heading off for city abroad
- Drives up the wall in French town
- French city risks deposing duke
- Provokes backers when changing sides
- Rovers not No.1 — that’s City
- French city displeases
- French city does annoy
- Outrages and risks being ignored by leader
- Gets cross in French city
- Gets annoyed and risks ignoring leader
Buddy explains!

The straight part
We know that "Outrages" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case outrages = angers.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 ANGERS mean?
ANGERS noun- A strong feeling of displeasure, hostility or antagonism towards someone or something, usually combined with an urge to harm.
- Pain or stinging.
- To cause such a feeling of antagonism in.
- To become angry.