The most common and most likely answer to this crossword clue is the 8 letter word AQUANAUT
I've seen this crossword clue in The Times
A
Q
U
A
N
A
U
T
More clues leading to the result AQUANAUT
Buddy explains!

The straight part
We know that "Diver" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case diver = aquanaut.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 AQUANAUT mean?
AQUANAUT noun- An underwater explorer.