Advance made by pair pursued by monster (8)
I believe the answer is:
progress
'advance' is the definition.
(to progress is to advance)
'pair pursued by monster' is the wordplay.
'pair' becomes 'pr' (abbreviation).
'pursued by' says to put letters next to each other.
'monster' becomes 'ogress' (female ogre).
'pr'+'ogress'='PROGRESS'
'made by' acts as a link.
(Other definitions for progress that I've seen before include "Course" , "Breakthrough - advance" , "Get on with" , "Gradual improvement or development" , "Forward movement towards a destination or goal" .)