The most common and most likely answer to this crossword clue is the 6 letter word UNKIND
I've seen this crossword clue in The Guardian
U
N
K
I
N
D
More clues leading to the result UNKIND
- A foreign character seen as savage
- Heartless family supporting article in Le Monde
- Drunk in dry section is nasty
- Somewhat drunk in defeat and thus unfeeling
- A French class that’s unfriendly
- No piano in Sex Pistols’ music and one new chord — or is that harsh?
- A foreign type beastly to others?
- World Body, generous, though uncharitable
- A French family with daughter showing no mercy
- Cruel, a Parisian child nicking note
Buddy explains!

The straight part
We know that "nasty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nasty = unkind.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 UNKIND mean?
UNKIND adjective- Lacking kindness, sympathy, benevolence, gratitude, or similar; cruel, harsh or unjust; ungrateful.
- Not kind; contrary to nature or type; unnatural.
- Having no race or kindred; childless.