Prohibition, sweetheart noted, would be a pain in the neck, perhaps (4)
I believe the answer is:
bane
'noted would be a pain in the neck perhaps' is the definition.
I can't tell whether this definition defines the answer.
'prohibition sweetheart' is the wordplay.
'prohibition' becomes 'ban' (ban is a kind of prohibition).
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'ban'+'e'='BANE'
Can you help me to learn more?
(Other definitions for bane that I've seen before include "Affliction, cause of distress" , "A fatal poison" , "Cause of great distress in a bean" , "Blight" , "Cause of trouble or worry, like bean" .)