Handing over the job to? (10)

I believe the answer is:

assignment

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'handing over' is the definition.
The answer and definition can be both acts as well as being singular nouns.
Perhaps you can see a link between them that I don't see?

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

Can you help me to learn more?

(Other definitions for assignment that I've seen before include "job" , "Task, piece of work" , "Task or duty" , "Duty to be done" .)

I've seen this clue in the Evening Standard.

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