Gives up, yet starts a new contract (7)

I believe the answer is:
resigns
'gives up' is the definition.
('resign' can be a synonym of 'give up')
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for resigns that I've seen before include "Leaves job voluntarily" , "Gives up (a post)" , "does the honourable thing" , "abdicates" .)
