Looking embarrassed about daughter (3)
I believe the answer is:
red
'looking embarrassed' is the definition.
(someone may go red when embarrassed)
'about daughter' is the wordplay.
'about' becomes 're' (regarding).
'daughter' becomes 'd' (genealogical abbreviation).
're'+'d'='RED'
(Other definitions for red that I've seen before include "Florid" , "Colour of 1 across" , "Ruby" , "Colour for danger" , "Very angry, seeing this" .)