Duty in paper round to turn up (4)
I believe the answer is:
onus
'duty' is the definition.
(thesaurus)
'paper round to turn up' is the wordplay.
'paper' becomes 'sun' (The Sun, UK newspaper).
'round' becomes 'o' (round can mean a round object).
'to turn up' shows that the letters should be reversed in order.
'sun'+'o'='suno'
'suno' in reverse letter order is 'ONUS'.
'in' acts as a link.
(Other definitions for onus that I've seen before include "'Burden, of proof (4)'" , "Duty or responsibility" , "Responsibilty" , "Weight of responsibility" , "albatross?" .)