Animal character from Greece captured by Dame (7)
I believe the answer is:
echidna
'animal' is the definition.
(echidna is a kind of animal)
'character from greece captured by dame' is the wordplay.
'character from greece' becomes 'chi' (chi is a Greek letter).
'captured by' means one lot of letters goes inside another.
'dame' becomes 'edna' (comedy character Dame Edna Everage).
'chi' inserted within 'edna' is 'ECHIDNA'.
(Other definitions for echidna that I've seen before include "Oz native" , "Spiny creature" , "Such a beast" , "Spiny egg-laying Australian mammal" , "Toothless type" .)