Gave written consent in bank with defeatist manner (10)

I believe the answer is:

resignedly

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'gave written consent in bank with defeatist manner' is the definition.
I can't tell whether this defines the answer.

'gave written consent in bank' is the wordplay.
'gave written consent' becomes 'signed'.
'in' indicates putting letters inside.
'bank' becomes 'rely' (I've seen this before).
'signed' going into 'rely' is 'RESIGNEDLY'.

Can you help me to learn more?

(Another definition for resignedly that I've seen is " without complaining".)

I've seen this clue in The Telegraph.

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