He gets money from dad the old-fashioned way (5)
I believe the answer is:
Here is my best explanation:
'he gets money' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'dad the old-fashioned way' is the wordplay.
'dad' becomes 'pa' ('pa' can be a synonym of 'dad').
'the old' becomes 'ye'.
'fashioned way' becomes 'e' (I can't justify this - if you can you should give a lot more credence to this answer).
'from' acts as a link.
(Other definitions for payee that I've seen before include "receiver", "One given money", "I'll get ready", "Beneficiary", "To whom cheque is written", "Recipient of money", "He gets the dough", "One receiving money", "Person to whom money is made out" and "Receiver of money".)