Delicate, discreet (7)
I believe the answer is:
tactful
I believe this clue is a double definition.
'delicate' is the first definition.
(I've seen this before)
'discreet' is the second definition.
(similar in meaning)
(Other definitions for tactful that I've seen before include "Showing sensitivity towards others" , "Like diplomat" , "Sensitive to others on difficult issues" , "using diplomacy" , "Polite" .)