By which you start to lay claim to the pillow? (4,7)
I believe the answer is:
down payment
'pillow?' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for down payment that I've seen before include "first instalment" , "Deposit towards a purchase" , "Start of settlement" .)