Disorder putting off old woman and another woman (4)
I believe the answer is:
lady
'woman' is the definition.
(lady is a kind of woman)
'disorder putting off old woman' is the wordplay.
'disorder' becomes 'malady' (malady is a kind of health problem).
'putting off' suggests deleting specific letters.
'old woman' becomes 'ma' (both can mean someone's mother).
'malady' with 'ma' taken away is 'LADY'.
'and another' is the link.
(Other definitions for lady that I've seen before include "Gentlewoman" , "Luck, for example" , "See 20" , "Woman, of refinement perhaps" , "High-class woman" .)