Family type looking embarrassed (7)
I believe the answer is:
kindred
'family' is the definition.
(kindred means one's relatives)
'type looking embarrassed' is the wordplay.
'type' becomes 'kind' (I've seen this in another clue).
'looking embarrassed' becomes 'red' (someone may go red when embarrassed).
'kind'+'red'='KINDRED'
(Other definitions for kindred that I've seen before include "Affinity" , "Similarity in character" , "clan" , "Related (people)" , "Related by blood or marriage" .)