Desperate thing to do (4,4)
I believe the answer is:
lose hope
'do' is the definition.
Although both the answer and definition are verbs in their base form, I don't see how they can define each other.
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for lose hope that I've seen before include "Become pessimistic" , "Despair" .)