Having an impeccable reputation, say (5,8)

I believe the answer is:

above reproach

(Other definitions for above reproach that I've seen before include "Beyond criticism" , "Blameless -- totally honest" , "Too good for criticism" , "Not criticisable" , "of unimpeachable quality" .)

I've seen this clue in The New York Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.