The woman up the street (3)
I believe the answer is:
eva
'the woman' is the definition.
(woman's name)
'up the street' is the wordplay.
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'the street' becomes 'ave' (short for avenue).
'ave' written backwards gives 'EVA'.
(Other definitions for eva that I've seen before include "Female" , "-- Peron, Argentinian First Lady" , "girl appears" , "Little --, US pop singer" , "-- Braun, Hitler mistress" .)