I appreciate that setter regularly showing discernment (5)
I believe the answer is:
taste
'discernment' is the definition.
(having discernment is having good taste)
'i appreciate that setter regularly' is the wordplay.
'i appreciate that' becomes 'ta' (informal way of saying thank you).
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternate letters of 'setter' are 'ste'.
'ta'+'ste'='TASTE'
'showing' is the link.
(Other definitions for taste that I've seen before include "Small sample of food" , "Perceive the flavour" , "Show sense" , "Partake of" , "Savour, relish" .)