Scoffed following daughter's engagement (4)
I believe the answer is:
date
'engagement' is the definition.
('date' can be a synonym of 'engagement')
'scoffed following daughter's' is the wordplay.
'scoffed' becomes 'ate' ('to scoff' is to eat).
'following' says to put letters next to each other.
'daughter' becomes 'd'.
'ate' after 'd' is 'DATE'.
(Other definitions for date that I've seen before include "For example, sell by" , "Particular time of event - fruit" , "Oval fruit" , "retrieved from palmtop?" , "Particular day" .)