Promise to go with you to the grave, perhaps (9)

I believe the answer is:

undertake

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'promise' is the definition.
(I know that undertake is a type of promise)

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for undertake that I've seen before include "Attempt to perform" , "Guarantee" , "what indisciplined motorway driver might do?" , "Accept - promise" , "Try" .)

I've seen this clue in The Telegraph.

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