The most common and most likely answer to this crossword clue is the 7 letter word POUTING
I've seen this crossword clue in The Guardian
P
O
U
T
I
N
G
Buddy explains!
The straight part
We know that "Looking offended" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case looking offended = pouting.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 POUTING mean?
POUTING verb- To push out one's lips.
- To thrust itself outward; to be prominent.
- To be or pretend to be ill-tempered; to sulk.
- To say while pouting.
- To shoot poults.
- An expression or motion that pouts; a pout.
- A fish in the cod family (Gadidae), Trisopterus luscus.