The most common and most likely answer to this crossword clue is the 5 plus 3 letter word THANK YOU
I've seen this crossword clue in The Daily Telegraph
T
H
A
N
K
Y
O
U
More clues leading to the result THANK YOU
- Much appreciated handkerchief during short tour
- Much obliged to a hunky jockey
- Words of gratitude for turning out and embracing rather improper behaviour – not half!
- Most of the UN okay changing response in present situation
- Sabotaged hunt okay to provide gift
- A youth moving to catch knight, then king, cheers
- One might say this very much as an expression of gratefulness
- Tailor out to mask thin piece of cloth, I appreciate that
- Show of appreciation given to a hunky doctor
- Cheers as handkerchief is in, out, shaken all about
Buddy explains!

The straight part
We know that "gift" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gift = thank you.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 THANK YOU mean?
THANK YOU noun- An expression of gratitude.
- (as a modifier before a noun) That expresses thanks.