The most common and most likely answer to this crossword clue is the 10 letter word PACHYDERMS
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result PACHYDERMS
Buddy explains!

The straight part
We know that "elephants" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case elephants = pachyderms.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 PACHYDERMS mean?
PACHYDERMS noun- A member of the obsolete taxonomic order Pachydermata, grouping of thick-skinned, hoofed animals such as the rhinoceros, hippopotamus, elephant, pig and horse.
- An elephant
- A person with thick skin; someone who is not affected by or does not care what others say about him or her.
- Someone who is insensitive.