The most common and most likely answer to this crossword clue is the 6 letter word FIZGIG
I've seen this crossword clue in The Guardian
F
I
Z
G
I
G
More clues leading to the result FIZGIG
Buddy explains!

The straight part
We know that "old minx" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old minx = fizgig.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 FIZGIG mean?
FIZGIG noun- A flirtatious, coquettish girl, inclined to gad or gallivant about; a gig, a giglot, a jillflirt.
- Something frivolous or trivial; a gewgaw, a trinket.
- To roam around in a frivolous manner; to gad about, to gallivant.
- A small squib-like firework that explodes with a fizzing or hissing noise.
- A spear with a barb on the end of it, used for catching fish; a type of harpoon.
- A police informer, a stool pigeon, someone employed by police to entrap someone elseor provoke them to commit a crime.
- To act as a police informer or agent provocateur.
- The common ragwort (Jacobaea vulgaris).