The most common and most likely answer to this crossword clue is the 10 letter word PROSPEROUS
I've seen this crossword clue in The Times
P
R
O
S
P
E
R
O
U
S
More clues leading to the result PROSPEROUS
- Doing well in Duke of Milan's university
- Wealthy US proposer involved
- Rich oppress our organising
- Rich American pursuing Miranda’s father
- Rich American follows Shakespearean
- Andre ultimately overwhelmed by poor Spurs failing to become successful
- Guardian supporting Shakespearean character faring well
- Wealthy professionals drinking super old cocktail
- Well-heeled American should follow the Duke of Milan
- Well-to-do island ruler meets under-secretary
Buddy explains!

The straight part
We know that "Rich" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rich = prosperous.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 PROSPEROUS mean?
PROSPEROUS adjective- Characterized by success
- Well off; affluent
- Favorable