Controversial part of PhD is put edifyingly (8)
I believe the answer is:
disputed
'controversial' is the definition.
(similar in meaning)
'part of phd is put edifyingly' is the wordplay.
'part of' indicates the answer is hidden within the clue.
'DISPUTED' can be found hidden inside 'phd is put edifyingly'.
(Other definitions for disputed that I've seen before include "Subject to disagreement and debate" , "Questioned, challenged veracity" , "Quarrelled over" , "Argued (about)" .)