Loath to serve a drunk (6)
I believe the answer is:
averse
'loath' is the definition.
(I know that loath can be written as averse)
'serve a drunk' is the wordplay.
'drunk' indicates an anagram.
'serve'+'a'='servea'
'servea' anagrammed gives 'AVERSE'.
'to' acts as a link.
(Other definitions for averse that I've seen before include "Disinclined, maybe to hard work" , "Hostile" , "Having a strong dislike" , "'Opposed, disinclined (6)'" , "Disinclined or reluctant" .)