Make a payment one has the right to give out (5)
I believe the answer is:
remit
'make a payment' is the definition.
(remitting is a kind of making a payment)
'right to give out' is the wordplay.
'right' becomes 'r' (common abbreviation).
'to give out' becomes 'emit' ('emit' can be a synonym of 'give out').
'r'+'emit'='REMIT'
'one has the' is the link.
(Other definitions for remit that I've seen before include "Scope of reference" , "Scope - send money" , "Give up" , "Send (money) by post" , "Send; abate; cancel" .)