The most common and most likely answer to this crossword clue is the 11 letter word TIMEKEEPERS
I've seen this crossword clue in The Daily Telegraph
T
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Buddy explains!

The straight part
We know that "Watches/conductors" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case watches/conductors = timekeepers.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 TIMEKEEPERS mean?
TIMEKEEPERS noun- A device that shows the time; a timepiece.
- A person who keeps records of the hours of attendance of employees.
- A person who records the time elapsed in a sporting event.
- (usually with adjective) A person (or something controlled by a person) that is or isn't punctual.