The most common and most likely answer to this crossword clue is the 4 letter word DONS
I've seen this crossword clue in Independent
D
O
N
S
More clues leading to the result DONS
Buddy explains!

The straight part
We know that "Puts on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case puts on = dons.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 DONS mean?
DONS noun- A title formerly borne by member of the high nobility of Portugal and Brazil
- A university professor, particularly one at Oxford or Cambridge.
- An employee of a university residence who lives among the student residents.
- A mafia boss.
- Any man, bloke, dude.
- (clothing) To put on, to dress in.