The most common and most likely answer to this crossword clue is the 6 letter word TOODLE
I've seen this crossword clue in The Times
T
O
O
D
L
E
More clues leading to the result TOODLE
- See you at that party hosting stars
- Advice on fluffy dog from Spooner? I’m off!
- Spooner's dog, pointer, so long
- Farewell party visited by Pope, also earlier
- Take care of Spooner’s dog — pointer
- Bottom of lost, powerless lackey getting hit for so long
- What to say when leaving dog — advice from Spooner
- Small Executive Officer too old to blend in gives an informal farewell
- Spooner’s dog advice cheers
- Farewell comment also suppressing lots
Buddy explains!

The straight part
We know that "See you" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case see you = toodle.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.