The most common and most likely answer to this crossword clue is the 7 letter word HOSTESS
I've seen this crossword clue in The Guardian
H
O
S
T
E
S
S
More clues leading to the result HOSTESS
- Society girl pursuing house party organiser
- Note about groups backing entertainer
- Entertainer delivered tango in stockings and smalls
- One who entertains army without leaving the front
- Hardy character on Tube briefly welcoming woman
- Ordinary end to Mrs T — “Nazi” to describe woman running party
- Entertaining woman in stockings — time to get extremely suspicious
- One giving party among toffs’ set, so hard up
- Lady issuing invitations — thus husband is upset about groups turning up
- Sexy curvy character including sex, initially?
Buddy explains!

The straight part
We know that "woman running party" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case woman running party = hostess.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 HOSTESS mean?
HOSTESS noun- A female host.
- A female innkeeper.
- Stewardess: a woman steward on an airplane.
- A bar hostess or bargirl; a paid female companion offering conversation and in some cases sex.
- To host, as a woman.