Curse out of loathing (4)
I believe the answer is:
oath
'curse' is the definition.
(I know that curse can be written as oath)
'of loathing' is the wordplay.
'of' indicates the answer is hidden within the clue.
'OATH' can be found hidden inside 'loathing'.
'out' is the link.
(Other definitions for oath that I've seen before include "Swearword or solemn promise" , "Solemn vow" , "A curse or solemn declaration" , "Courtroom promise" , "blasphemy" .)