The most common and most likely answer to this crossword clue is the 9 letter word PRIVILEGE
I've seen this crossword clue in Independent
P
R
I
V
I
L
E
G
E
More clues leading to the result PRIVILEGE
- Priest, say, cutting one abhorrent benefit
- Puritan, English, accepting detestable social advantage
- Cooked pig liver, edible starter? That’s right
- One annoyingly smug about unpleasant people ultimately right?
- I’ve gripe possibly about introduction of lawyer’s immunity claim?
- Special pleasure for puritan to seize loathsome drug
- Gripe at work about iniquitous special treatment
- Right status symbol
- Gripe terribly about loathsome advantage enjoyed by some
- Woeful gripe about wicked entitlement
Buddy explains!

The straight part
We know that "immunity claim?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case immunity claim? = privilege.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 PRIVILEGE mean?
PRIVILEGE noun- (ecclesiastical law) An exemption from certain laws granted by the Pope.
- A particular benefit, advantage, or favor; a right or immunity enjoyed by some but not others; a prerogative, preferential treatment.
- An especially rare or fortunate opportunity; the good fortune (to do something).
- The fact of being privileged; the status or existence of (now especially social or economic) benefit or advantage within a given society.
- A right or immunity enjoyed by a legislative body or its members.
- A stock market option.
- A common law doctrine that protects certain communications from being used as evidence in court.
- An ability to perform an action on the system that can be selectively granted or denied to users.
- To grant some particular right or exemption to; to invest with a peculiar right or immunity; to authorize
- To bring or put into a condition of privilege or exemption from evil or danger; to exempt; to deliver.