Advance publicity covering monstrous female (8)
I believe the answer is:
progress
'advance' is the definition.
('progress' can be a synonym of 'advance')
'publicity covering monstrous female' is the wordplay.
'publicity' becomes 'pr'.
'covering' says to put letters next to each other (on top of in down clue).
'monstrous female' becomes 'ogress' (I've seen this before).
'pr'+'ogress'='PROGRESS'
(Other definitions for progress that I've seen before include "Course" , "Get on with" , "Forward movement towards a destination or goal" , "Advancement" , "Advance - movement" .)