Put down what is correct, we hear (5)
I believe the answer is:
write
'put down' is the definition.
(I know that write is a more specific form of the action record)
'correct we hear' is the wordplay.
'correct' becomes 'right' (right can mean correct).
'we hear' shows a homophone (sound like).
'right' sounds like 'WRITE'.
'what is' is the link.
(Other definitions for write that I've seen before include "Produce text" , "Draft" , "Jot" , "Use a pen/pencil" , "Put pen to paper" .)