The most common and most likely answer to this crossword clue is the 7 letter word FASTING
I've seen this crossword clue in The Times
F
A
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T
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Buddy explains!

The straight part
We know that "Eating nothing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eating nothing = fasting.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 FASTING mean?
FASTING verb- To restrict one’s personal consumption, generally of food, but sometimes other things, in various manners (totally, temporally, by avoiding particular items), often for religious or medical reasons.
- Abstinence from food