Authority of a bishop getting grip (7)
I believe the answer is:
arbiter
'authority' is the definition.
(I know that arbiter is a type of evaluator)
'a bishop getting grip' is the wordplay.
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'getting' is an insertion indicator.
'grip' becomes 'bite' (biting is a kind of gripping).
'rr' going around 'bite' is 'rbiter'.
'a'+'rbiter'='ARBITER'
'of' acts as a link.
(Other definitions for arbiter that I've seen before include "Rear bit (anag.)" , "One has the authority to settle disputes" , "One has the authority to resolve disputes" , "Source of authority" , "Settler of dispute" .)