What might confer a degree of tact when cutting cold Yankee (7)
I believe the answer is:
diploma
'what might confer a degree' is the definition.
(a diploma is a certificate for an academic degree)
I don't understand the rest of the clue.
(Other definitions for diploma that I've seen before include "official document" , "Honorific document" , "Course certificate" , "Certificate awarded by college for educational attainment" , "Degree document" .)