Staff take more time to deal with deliveries (5)

I believe the answer is:

baton

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'staff' is the definition.
(I know that baton is a type of staff)

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for baton that I've seen before include "Stick passed in relay races" , "Conductor's rod" , "Relay runner's stick" , "It's passed in a relay race" , "Prohibition" .)

I've seen this clue in The Times.

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