The most common and most likely answer to this crossword clue is the 2 plus 4 letter word SO LONG
I've seen this crossword clue in The Sunday Telegraph
S
O
L
O
N
G
More clues leading to the result SO LONG
- Athenian statesman with good parting words
- Very protracted farewell
- Farewell rendition by one singer no good
- Farewell piece about heartless Lothario
- Tune incorporating final parts of Hello Goodbye
- Phrase used on leaving single northern girl, initially
- Words on parting very much in need of a trim?
- See you alone with nothing, gutted
- Farewell performance Nijinsky gave for beginners
- Performance extremely numbing, I’m heading for the exit!
Buddy explains!

The straight part
We know that "Words on parting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case words on parting = so long.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.