For her, partner (not male) not available (4)
I believe the answer is:
anna
'for her' is the definition.
(I've seen this before)
I don't understand how the remainder of the clue works.
(Other definitions for anna that I've seen before include "Palindromic girl's name" , "Miss Karenina" , "She's a woman, whichever way you look at it" , "Dame -- Neagle" , "Unit of length" .)