Give up on board divulging information? (6)
I believe the answer is:
resign
'give up' is the definition.
(I know this)
'on board divulging information?' is the wordplay.
I cannot really see how this works, but
'on' could be 're' ('on' can be mean 'with reference to') and 're' is found in the answer.
'board' could be 'sign' (I've seen this in other clues) and 'sign' is found in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for resign that I've seen before include "Either leave" , "Abdicate" , "Stand down" , "Give up office" , "Hand in one's notice" .)