Either leave the office or put your name to another contract (6)
I believe the answer is:
resign
'either leave' is the definition.
(I've seen this before)
'another contract' is the wordplay.
'another' becomes 're' (I've seen this in other clues).
'contract' becomes 'sign' (signing is a kind of contracting).
're'+'sign'='RESIGN'
'the office or put your name to' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for resign that I've seen before include "Give up one's job" , "Either leave" , "Hand in one's notice" , "Give up one's post" , "advice for the incompetent?" .)