Old woman upset over exam lacking principles (6)
I believe the answer is:
amoral
'lacking principles' is the definition.
(I've seen this before)
'old woman upset over exam' is the wordplay.
'old woman' becomes 'ma' (both can mean someone's mother).
'upset' is a reversal indicator.
'over' means one lot of letters go next to another.
'exam' becomes 'oral' (spoken academic test).
'ma' reversed gives 'am'.
'am'+'oral'='AMORAL'
(Other definitions for amoral that I've seen before include "Lacking a sense of right and wrong" , "Unprincipled" , "Unscrupulous" , "Without sense of right and wrong" , "Shameless" .)