About to sing drunkenly and give up (6)
I believe the answer is:
resign
'give up' is the definition.
(I know that give up can be written as resign)
'about to sing drunkenly' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'drunkenly' indicates anagramming the letters.
'sing' anagrammed gives 'sign'.
're'+'sign'='RESIGN'
'and' acts as a link.
(Other definitions for resign that I've seen before include "Give up one's post" , "Quit" , "Either leave" , "Turn over" , "Stand down" .)