The most common and most likely answer to this crossword clue is the 8 letter word HARRIDAN
I've seen this crossword clue in The Guardian
H
A
R
R
I
D
A
N
More clues leading to the result HARRIDAN
- Scold desperate man ousting Rex’s son?
- Difficult to forget the last and worst point about nag
- Hard rain disturbed shrew
- Shrewish woman badgered, some might say, a knight
- Virago shows impulsive desire in hot island
- Battle-axe? King and I protected by tough one
- Tough to maintain romance at first, one with an ogress
- Vixen kept secret article that’s arrived in the interim
- Nag hurt— 26 recalled
- Domineering woman and son dropping off type of tweed with short Scandinavian
Buddy explains!

The straight part
We know that "Nag" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nag = harridan.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 HARRIDAN mean?
HARRIDAN noun- A vicious and scolding woman, especially an older one.