The most common and most likely answer to this crossword clue is the 8 letter word HEAVENLY
I've seen this crossword clue in The Times
H
E
A
V
E
N
L
Y
More clues leading to the result HEAVENLY
Buddy explains!

The straight part
We know that "divine" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case divine = heavenly.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 HEAVENLY mean?
HEAVENLY adjective- Relating to the sky or outer space, regarded as the realm of the sun, moon, planets, and stars.
- Of or pertaining to the highest degree of glory.
- Of or pertaining to the heaven believed in by many religions.
- Of or pertaining to the kingdom of God; divine.
- Strongly or sublimely beautiful or pleasurable.
- In a manner like that of heaven; by the influence or agency of heaven; divinely, miraculously.
- To a degree such as to elicit great pleasure.