Son cooking made a chef embarrassed (10)
I believe the answer is:
shamefaced
'embarrassed' is the definition.
(thesaurus)
'son cooking made a chef' is the wordplay.
'son' becomes 's'.
'cooking' indicates an anagram.
'made'+'a'+'chef'='madeachef'
'madeachef' with letters rearranged gives 'hamefaced'.
's'+'hamefaced'='SHAMEFACED'
(Other definitions for shamefaced that I've seen before include "Red" , "Sorry-looking" , "Very modest, bashful" , "Sheepish" , "Embarrassed" .)