The most common and most likely answer to this crossword clue is the 5 letter word PRADA
I've seen this crossword clue in The Times
P
R
A
D
A
More clues leading to the result PRADA
- Milan outfit quietly training players
- Red paper out of very fashionable company
- Artist and daughter wearing relative’s fashion label
- Fashion house with power over aspiring drama queens?
- Italian fashion label popular primarily with drama group
- 11's preferred fashion brand excellent, Dad admits
- Dad incorporates cool fashion house
Buddy explains!

The straight part
We know that "Milan outfit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case milan outfit = prada.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.