Complete postgrad degree covering empire (6)
I believe the answer is:
domain
'empire' is the definition.
(I know that empire can be written as domain)
'complete postgrad degree covering' is the wordplay.
I cannot really understand how this works, but
'complete' could be 'do' (doing is a kind of completing) and 'do' is found in the answer.
'degree' could be 'ma' (Master of Arts is a type of degree) and 'ma' is found in the answer.
The remaining letters 'in' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
(Other definitions for domain that I've seen before include "Area under someone's control, field of activity" , "Sphere of activity" , "Territory over which rule or control is exercised" , "Range of influence or field of activity" , "Range of influence or field of thought" .)