The most common and most likely answer to this crossword clue is the 10 letter word ESCAPEMENT
I've seen this crossword clue in The Times
E
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More clues leading to the result ESCAPEMENT
Buddy explains!

The straight part
We know that "Watch part" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case watch part = escapement.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 ESCAPEMENT mean?
ESCAPEMENT noun- The contrivance in a timepiece (winding wristwatch) which connects the train of wheel work with the pendulum or balance, giving to the latter the impulse by which it is kept in vibration.
- A mechanism found in devices such as a typewriter or printer which controls lateral motion of the carriage.
- An escape or means of escape.
- The number of fish that escape commercial fishing operations and travel upstream to spawn.