Awful singer to pack it in (6)
I believe the answer is:
resign
'pack it in' is the definition.
(eg to pack a job in is to resign)
'awful singer' is the wordplay.
'awful' indicates anagramming the letters.
'singer' is an anagram of 'RESIGN'.
'to' is the link.
(Other definitions for resign that I've seen before include "withdraw" , "Give up position" , "admit defeat" , "Give up office" , "Give up one's post" .)