Bishop is not in good shape making way through the house (4)
I believe the answer is:
bill
'good shape making way through the house' is the definition.
I can't judge whether this definition defines the answer.
'bishop is not' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'is not' becomes 'ill' (I can't explain this - if you can you should give a lot more credence to this answer).
'b'+'ill'='BILL'
'in' acts as a link.
Can you help me to learn more?
(Other definitions for bill that I've seen before include "Promontory; beak" , "informing of damage" , "Law proposal" , "Reckoning" , "Poster' charge" .)