The most common and most likely answer to this crossword clue is the 5 letter word RUSTS
I've seen this crossword clue in The Times
R
U
S
T
S
Buddy explains!
The straight part
We know that "Picks up brown coat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case picks up brown coat = rusts.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 RUSTS mean?
RUSTS noun- The deteriorated state of iron or steel as a result of moisture and oxidation.
- A similar substance based on another metal (usually with qualification, such as "copper rust").
- A reddish-brown color.
- A disease of plants caused by a reddish-brown fungus.
- Damage caused to stamps and album pages by a fungal infection.
- To oxidize, especially of iron or steel.
- To cause to oxidize.
- To be affected with the parasitic fungus called rust.
- To (cause to) degenerate in idleness; to make or become dull or impaired by inaction.