Desperate thing to do (4,4)

I believe the answer is:

lose hope

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'do' is the definition.
Although both the answer and definition are verbs in their base form, I don't understand how one could define the other.

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

Can you help me to learn more?

(Other definitions for lose hope that I've seen before include "Become pessimistic" , "Despair" .)

I've seen this clue in the Evening Standard.

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