Nanny Greek character admires terribly (9)
I believe the answer is:
nursemaid
'nanny' is the definition.
(both can mean someone who looks after children)
'greek character admires terribly' is the wordplay.
'greek character' becomes 'nu' (letter from the Greek alphabet).
'terribly' indicates anagramming the letters.
'admires' anagrammed gives 'rsemaid'.
'nu'+'rsemaid'='NURSEMAID'
(Other definitions for nursemaid that I've seen before include "Woman employed to look after children" , "One employed to care for small children" , "caretaker" , "her charges are small" , "employ one for small charge" .)