Accept responsibility of arranging funeral? (9)

I believe the answer is:

undertake

'accept responsibility' is the definition.
(undertake to complete a task)

I cannot understand how the remainder of the clue works.

(Other definitions for undertake that I've seen before include "Guarantee" , "Agree or promise to do something" , "Enter upon an activity" , "pass on the wrong side?" , "Set about" .)

I've seen this clue in The Times.

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