The most common and most likely answer to this crossword clue is the 7 letter word DIGNIFY
I've seen this crossword clue in Independent
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Buddy explains!

The straight part
We know that "Exalt" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case exalt = dignify.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 DIGNIFY mean?
DIGNIFY verb- To invest with dignity or honour.
- To give distinction to.
- To exalt in rank.
- (chiefly in the negative) To treat as worthy or acceptable; to indulge or condone by acknowledging.