A woman alone or otherwise (7)
I believe the answer is:
leonora
'a woman' is the definition.
'alone or otherwise' is the wordplay.
'otherwise' is an anagram indicator.
'alone'+'or'='aloneor'
'aloneor' is an anagram of 'LEONORA'.
(Other definitions for leonora that I've seen before include "Girl" , "Name of woman" , "Girl's name; or alone (anag.)" , "Heroine of Beethoven's Fidelio" .)