Unethical having exam in the morning (6)
I believe the answer is:
amoral
'unethical' is the definition.
(I've seen this before)
'exam in the morning' is the wordplay.
I cannot really see how this works, but
'exam' could be 'oral' (spoken academic test) and 'oral' is found in the answer.
'morning' could be 'am' and 'am' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'having' acts as a link.
(Other definitions for amoral that I've seen before include "Ignoring what's right and wrong" , "Without ethics" , "Without an ethical code" , "Unconcerned about what's right or wrong" , "Lacking any ethical standards" .)