Writer's rubbish hotel (4)
I believe the answer is:
roth
'writer's' is the definition.
(I have seen 'American writer' mean 'roth' so perhaps 'writer' could also mean 'roth')
'rubbish hotel' is the wordplay.
'rubbish' becomes 'rot' (both can mean nonsense).
'hotel' becomes 'h' (phonetic alphabet: alpha, bravo, charlie etc.).
'rot'+'h'='ROTH'
(Other definitions for roth that I've seen before include "Portnoy's Complaint author, d. 2018" , "American Jewish novelist, Philip, b. 1933" , "Philip --, US author" , "Author of Portnoy's Complaint, b. 1933" , "American writer" .)