Supervise a review that is influential (10)
I believe the answer is:
'is influential' is the definition.
'supervise a review' is the wordplay.
'review' is an anagram indicator.
'supervisea' with letters rearranged gives 'PERSUASIVE'.
'that' is the link.
(Other definitions for persuasive that I've seen before include "Convincing" , "Providing sound reasoning" .)