Having a good reputation (4-7-2)
I believe the answer is:
well-thought-of
'having a good reputation' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for well-thought-of that I've seen before include "Esteemed" , "Highly regarded" , "Highly-regarded" , "Having a good reputation" , "Respected" .)