The most common and most likely answer to this crossword clue is the 7 letter word FAINTED
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More clues leading to the result FAINTED
Buddy explains!

The straight part
We know that "Writer’s exhausted" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case writer’s exhausted = fainted.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 FAINTED mean?
FAINTED verb- To lose consciousness through a lack of oxygen or nutrients to the brain, usually as a result of suddenly reduced blood flow (may be caused by emotional trauma, loss of blood or various medical conditions).
- To sink into dejection; to lose courage or spirit; to become depressed or despondent.
- To decay; to disappear; to vanish.