The most common and most likely answer to this crossword clue is the 7 letter word FATTEST
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The straight part
We know that "Most elephantine" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most elephantine = fattest.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 FATTEST mean?
FATTEST adjective- Carrying more fat than usual on one's body; plump; not lean or thin.
- Thick.
- Bountiful.
- Oily; greasy; unctuous; rich (said of food).
- Exhibiting the qualities of a fat animal; coarse; heavy; gross; dull; stupid.
- Fertile; productive.
- Rich; producing a large income; desirable.
- Abounding in riches; affluent; fortunate.
- Of a character which enables the compositor to make large wages; said of matter containing blank, cuts, or many leads, etc.
- (originally African American Vernacular English) Excellent; cool; very good.
- Sexy.
- Rich in texture; prominent.