Hard up, the woman's got the rent halved (6)
I believe the answer is:
severe
'hard' is the definition.
(I've seen this before)
'up the woman's got the rent halved' is the wordplay.
'up' is a reversal indicator (in down clue: letters go upwards).
'the woman's' becomes 'eves' (Eve is an example**).
'got' is a charade indicator (letters next to each other).
'halved' means to take half the letters.
'eves' reversed gives 'seve'.
'rent' with half the letters taken is 're'.
'seve'+'re'='SEVERE'
(Other definitions for severe that I've seen before include "Serious or strict" , "Very plain in style or appearance" , "Harsh, rigorous" , "Terrible" , "Formal - unsmiling" .)