Vigil peer arranged? That’s right (9)
I believe the answer is:
privilege
'right' is the definition.
(privilege can mean a right to do something)
'vigil peer arranged?' is the wordplay.
'arranged?' indicates anagramming the letters.
'vigil'+'peer'='vigilpeer'
'vigilpeer' with letters rearranged gives 'PRIVILEGE'.
'that's' acts as a link.
(Other definitions for privilege that I've seen before include "Special right" , "Honour" , "conditional benefit?" , "Special advantage" , "Favour not available to all" .)