The most common and most likely answer to this crossword clue is the 6 letter word VEGANS
I've seen this crossword clue in Independent
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More clues leading to the result VEGANS
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The straight part
We know that "those on a diet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case those on a diet = vegans.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 VEGANS mean?
VEGANS noun- A person who does not eat, drink or otherwise consume any animal products
- A person committed to avoiding products and practices that inherently involve animal use, including all foods containing animal products, and to abstaining from direct and intentional harm to animals as far as possible; an adherent to veganism.