The most common and most likely answer to this crossword clue is the 11 letter word MILLIONAIRE
M
I
L
L
I
O
N
A
I
R
E
Buddy explains!

The straight part
We know that "wealthy person" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wealthy person = millionaire.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 MILLIONAIRE mean?
MILLIONAIRE noun- (strictly) A person whose net worth is at or greater than one million units of the local currency, but less than two million.
- A person whose net worth is at or greater than one million units of the local currency; a multimillionaire.