The most common and most likely answer to this crossword clue is the 7 letter word ARIADNE
I've seen this crossword clue in Independent
A
R
I
A
D
N
E
More clues leading to the result ARIADNE
- Song complete that’s elevated one assisting 25
- A final appearance upset Greek maiden
- Song with finale about woman Theseus abandoned
- Greek opera feature perhaps done – nothing missing
- King of Crete’s daughter and I are drunk
- Operatic heroine‘s number to finish up
- Lover of Theseus gives song with uplifting finale
- Greek princess in song, bottom raised
- Clue provider‘s strain to stop in retirement
- Song finale recalled opera heroine
Buddy explains!

The straight part
We know that "King of Crete’s daughter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case king of crete’s daughter = ariadne.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.