Grilling (5,6)
I believe the answer is:
third degree
'grilling' is the definition.
(I have seen 'Intense grilling' mean 'third degree' so perhaps 'grilling' could also mean 'third degree')
This is the entire clue.
(Other definitions for third degree that I've seen before include "Demanding viva" , "Post-doctorate" , "ruthless grilling" , "Demanding quiz" , "doctorate, perhaps" .)