The most common and most likely answer to this crossword clue is the 11 letter word NYMPHOMANIA
I've seen this crossword clue in The Guardian
N
Y
M
P
H
O
M
A
N
I
A
More clues leading to the result NYMPHOMANIA
Buddy explains!
The straight part
We know that "Woman’s obsession for the other" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case woman’s obsession for the other = nymphomania.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does NYMPHOMANIA mean?
NYMPHOMANIA noun- Excess of sexual behaviour or desire in women.