His useless house is short of rations! (7)
I believe the answer is:
horatio
'his useless' is the definition.
The definition suggests a singular noun which matches the answer.
'house is short of rations' is the wordplay.
'house' becomes 'ho' (abbreviation for house).
'is short of rations' becomes 'ratio' (I can't justify this - if you can you should believe this answer much more).
'ho'+'ratio'='HORATIO'
Can you help me to learn more?
(Other definitions for horatio that I've seen before include "part of Hamlet" , "Hamlet's friend: Hornblower's first name" , "Speaker of Good night, sweet prince (Hamlet)" , "Nelson's first name" , "Hamlet''s friend - Nelson" .)