Art gallery frames initially showing discernment (5)
I believe the answer is:
taste
'discernment' is the definition.
(having discernment is having good taste)
'art gallery frames initially showing' is the wordplay.
'art gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'frames' is an insertion indicator (outside letters frame the inside letters).
'initially' says to take the initial letters.
The initial letter of 'showing' is 's'.
'tate' enclosing 's' is 'TASTE'.
(Other definitions for taste that I've seen before include "Experience - discrimination" , "choice" , "Sip" , "Fine discernment" , "bit to eat" .)