The most common and most likely answer to this crossword clue is the 8 letter word SHREWISH
I've seen this crossword clue in The Guardian
S
H
R
E
W
I
S
H
More clues leading to the result SHREWISH
- Run into woman with desire to be ill-natured
- Say nothing about preference for nagging
- Quiet about desire to be like Kate
- Ill-natured female retaining right to desire
- Scrap not ending with desire to be harridan-like
- Like Kate, she inspires rare desire
- Like Kate Moss, ultimately having desire to take her out?
- Say nothing about wife — is husband inclined to nag?
- Like a rodent‘s short cut, long
- Ill-tempered live wire has quiet sandwich
Buddy explains!

The straight part
We know that "harridan-like" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case harridan-like = shrewish.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 SHREWISH mean?
SHREWISH adjective- Of or pertaining to a shrew (a nagging, ill-tempered woman).
- Bad-tempered; ill-natured; obstinate, as a shrew.