Turn down; diminish (7)
I believe the answer is:
decline
I believe this is a double definition.
'turn down' is the first definition.
(I know that turn down can be written as decline)
'diminish' is the second definition.
(I know that decline is a more specific form of the action diminish)
(Other definitions for decline that I've seen before include "Refuse - to go down" , "Downturn - turn down" , "increasing weakness" , "Refuse to accept" , "The classics student must often" .)