Sensitivity (4)
I believe the answer is:
tact
'sensitivity' is the definition.
(being tactful is being sensitive)
This is the entire clue.
(Other definitions for tact that I've seen before include "Delicacy of feeling, skill in saying the right thing" , "measure of diplomacy?" , "Sensitivity, diplomacy" , "Skill in dealing with people" , "Consideration in dealing with others" .)