The most common and most likely answer to this crossword clue is the 3 plus 5 letter word FAT SHAME
I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "Embarrass person of substance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case embarrass person of substance = fat shame.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 FAT SHAME mean?
FAT SHAME verb- To deride or criticise someone's obesity.