Writer's essay — Milking in a New Way (8,4)
I believe the answer is:
kingsley amis
'writer's' is the definition.
I don't know anything about this answer so I can't tell whether this works.
'essay milking in a new way' is the wordplay.
'in a new way' indicates anagramming the letters.
'essay'+'milking'='essaymilking'
'essaymilking' anagrammed gives 'KINGSLEY AMIS'.
Can you help me to learn more?
(Other definitions for kingsley amis that I've seen before include ""Lucky Jim" author" , "novelist" .)