The most common and most likely answer to this crossword clue is the 12 letter word LEAVE-TAKING
I've seen this crossword clue in The Guardian
L
E
A
V
E
-
T
A
K
I
N
G
More clues leading to the result LEAVE-TAKING
Buddy explains!
The straight part
We know that "Saying goodbye" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case saying goodbye = leave-taking.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 LEAVE-TAKING mean?
LEAVE-TAKING noun- The process of saying goodbye.
- The act or process of taking leave (time away from work)