My Fair Lady lady (5)
I believe the answer is:
eliza
'my fair lady lady' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for eliza that I've seen before include "Henry Higgins' protege (My Fair Lady)" , "flower-girl in dramatic work" , "Miss Doolittle/s first name" , "Miss Doolittle" , "girl" .)