Old Greek city king rejected urgent appeal by child (7)
I believe the answer is:
knossos
'old greek city' is the definition.
(ancient Cretan city)
'king rejected urgent appeal by child' is the wordplay.
'king' becomes 'K' (abbreviation for king in chess).
'rejected' says the letters should be written in reverse.
'urgent appeal' becomes 'SOS' (an SOS is an emergency message).
'by' means one lot of letters go next to another.
'child' becomes 'son' (son is a kind of child).
'sos'+'son'='sosson'
'sosson' back-to-front is 'nossos'.
'k'+'nossos'='KNOSSOS'
(Other definitions for knossos that I've seen before include "Minoan ruin in Crete" , "tourist attraction in Med" , "Minoan site on Crete" , "Ancient Cretan city" , "labyrinth" .)