Used to be that lady's cleaner (6)
I believe the answer is:
washer
'cleaner' is the definition.
(I've seen this before)
'used to be that lady's' is the wordplay.
'used to be' becomes 'was' (eg 'he was...' means 'he used to be...').
'that lady' becomes 'her' ('her' refers to a woman).
'was'+'her'='WASHER'
(Other definitions for washer that I've seen before include "Baptist" , "Perhaps laundryman" , "Metal disc for hawser" , "Spacer for nut and bolt" , "Cleaner" .)