A sense of discernment (5)
I believe the answer is:
taste
I believe this is a double definition.
'a sense' is the first definition.
(taste is one of the five senses)
'discernment' is the second definition.
(having discernment is having good taste)
'of' is the link.
(Other definitions for taste that I've seen before include "Experience - discrimination" , "Discrimination - a sense" , "Dash" , "Savour in the mouth" , "gains experience" .)