The most common and most likely answer to this crossword clue is the 7 letter word NAMASTE
I've seen this crossword clue in The Guardian
N
A
M
A
S
T
E
Buddy explains!

The straight part
We know that "a greeting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a greeting = namaste.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 NAMASTE mean?
NAMASTE noun- The traditional greeting when saying the word namaste, with folded hands and a slight bow.
- In yoga, the pose associated with this word, usually with the flat hands held palms together, fingers up, in front of the heart and a slight bow.
- To utter "namaste".
- Literally "I bow to you"; used as a greeting or acknowledgement of the equality of all, which pays honor to the sacredness of all.