The most common and most likely answer to this crossword clue is the 5 letter word HELLO
I've seen this crossword clue in The Times
H
E
L
L
O
More clues leading to the result HELLO
- Greeting a man will love?
- The man will start to offer greeting
- How do royals dominate its pages?
- A greeting the chap is going to love
- He will ring in greeting
- Greeting seen when Rachel and Louise meet
- Welcome Shakespeare character books ignored
- Below-zero greeting?
- The man will love this magazine:
- I say the inferno’s nonexistent
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 = hello.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 HELLO mean?
HELLO noun- "Hello!" or an equivalent greeting.
- To greet with "hello".
- A greeting (salutation) said when meeting someone or acknowledging someone’s arrival or presence.
- A greeting used when answering the telephone.
- A call for response if it is not clear if anyone is present or listening, or if a telephone conversation may have been disconnected.
- Used sarcastically to imply that the person addressed or referred to has done something the speaker or writer considers to be foolish.
- An expression of puzzlement or discovery.