The most common and most likely answer to this crossword clue is the 3 letter word FOB
I've seen this crossword clue in The Times
F
O
B
Buddy explains!
The straight part
We know that "Watch may depend on it" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case watch may depend on it = fob.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 FOB mean?
FOB noun- A little pocket near the waistline of a pair of trousers or in a waistcoat or vest to hold a pocketwatch; a watch pocket.
- A short chain or ribbon to connect such a pocket to the watch.
- A small ornament attached to such a chain. (See Usage Notes below)
- A hand-held remote control device used to lock/unlock motor cars etc.
- To cheat, to deceive, to trick, to take in, to impose upon someone.
- To beat; to maul.