The most common and most likely answer to this crossword clue is the 4 plus 3 letter word WELL OFF
I've seen this crossword clue in The Guardian
W
E
L
L
O
F
F
More clues leading to the result WELL OFF
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 = well off.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.
Crossword Answer definitions
WELL OFF adjective- Of a person: in fortunate circumstances, especially having financial security; comfortably off.
- Of any item, in a good position or circumstance.