Dad has system of paying — such is his family duty (8)
I believe the answer is:
parental
'is his family duty' is the definition.
The definition suggests a singular noun but the answer is not.
'dad has system of paying' is the wordplay.
'dad' becomes 'pa' ('pa' can be a synonym of 'dad').
'has' says to put letters next to each other.
'system of paying' becomes 'rental'.
'pa'+'rental'='PARENTAL'
'such' is the link.
(Other definitions for parental that I've seen before include "like mum and dad" , "Relating to mother and father" , "Of mother and/or father" , "of father, perhaps" , "of old man and woman" .)