Delayed by father's sense of taste (6)
I believe the answer is:
palate
'sense of taste' is the definition.
(I've seen this before)
'delayed by father's' is the wordplay.
'delayed' becomes 'late' (I've seen this before).
'by' says to put letters next to each other.
'father' becomes 'pa' (pa is a kind of father).
'late' after 'pa' is 'PALATE'.
(Other definitions for palate that I've seen before include "Roof of the mouth, seat of taste" , "relish" , "Sense of taste at roof of mouth" , "having ability to appreciate good food" , "A plate (anag.)" .)