The most common and most likely answer to this crossword clue is the 4 letter word CLOY
C
L
O
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More clues leading to the result CLOY
Buddy explains!

The straight part
We know that "Be disgustingly rich" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case be disgustingly rich = cloy.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 CLOY mean?
CLOY verb- To fill up or choke up; to stop up.
- To clog, to glut, or satisfy, as the appetite; to satiate.
- To fill to loathing; to surfeit.