The most common and most likely answer to this crossword clue is the 10 letter word BACKSTITCH
I've seen this crossword clue in Independent
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More clues leading to the result BACKSTITCH
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The straight part
We know that "activity of the sewer (one sewing)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case activity of the sewer (one sewing) = backstitch.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.
Crossword Answer definitions
BACKSTITCH noun- A type of sewing stitch where the stitch goes backwards on the top side of the fabric and doubles forward on the bottom, coming out farther in front, then repeats. The backstitch is a very tight and secure stitch, and also looks very neat.
- To sew with a backstitch.