The most common and most likely answer to this crossword clue is the 7 letter word THRIVES
I've seen this crossword clue in The Daily Telegraph
T
H
R
I
V
E
S
Buddy explains!

The straight part
We know that "does well" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case does well = thrives.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 THRIVES mean?
THRIVES verb- To grow or increase stature; to grow vigorously or luxuriantly, to flourish.
- To increase in wealth or success; to prosper, be profitable.