The most common and most likely answer to this crossword clue is the 9 letter word WORKBENCH
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Buddy explains!
The straight part
We know that "Carpenter might apply herself at this" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case carpenter might apply herself at this = workbench.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 WORKBENCH mean?
WORKBENCH noun- A sturdy bench or table at which manual work is done by a carpenter, machinist, etc.