The most common and most likely answer to this crossword clue is the 10 letter word DEROGATORY
I've seen this crossword clue in The Guardian
D
E
R
O
G
A
T
O
R
Y
More clues leading to the result DEROGATORY
- Offering insults before leftist turns on rightist
- Offensive old goat misbehaving in part of Ulster
- Insulting aged or corrupt politician
- Offensive revolutionary deeply hurt a right-winger
- Blush over a Conservative being intentionally offensive
- A stuck-up politician, rude
- Embarrassed about own goal, a politician becomes offensive
- Disparaging past socialist turned Conservative
- Demeaning to regard you almost entirely in a stupid way
- Edgy orator at work that’s critical
Buddy explains!

The straight part
We know that "offensive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case offensive = derogatory.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 DEROGATORY mean?
DEROGATORY noun- A trade-line on a credit report that includes negative credit history.
- (usually with to) Tending to derogate:
- (of a clause in a testament) Being or pertaining to a derogatory clause.