Demand turning up, it's overdue (9)
I believe the answer is:
stipulate
'demand' is the definition.
(synonyms)
'turning up it's overdue' is the wordplay.
'turning' says the letters should be written backwards.
'overdue' becomes 'late' (similar in meaning).
'up'+'its'='upits'
'upits' backwards is 'stipu'.
'stipu'+'late'='STIPULATE'
(Other definitions for stipulate that I've seen before include "Specify as an essential part" , "Make a demand" , "Insist on as part of agreement" , "Specify as a condition or requirement" , "Define, require" .)