Crossword Genius

Stay alert but don't give timekeeper away! (4,5)

Ross

I believe the answer is:

keep watch

I'm a little stuck... Click here to teach me more about this clue!

'stay alert' is the definition.
(I've seen this before)

'don't give timekeeper away' is the wordplay.
I cannot quite see how this works, but
'timekeeper' could be 'watch' (watch is a kind of timekeeper) and 'watch' is located in the answer.
The remaining letters 'keep' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'but' is the link.

Can you help me to learn more?

(Other definitions for keep watch that I've seen before include "Hold vigil" , "Stay alert" , "hang on to timer" .)

I've seen this clue in the Sydney Morning Herald.
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