The most common and most likely answer to this crossword clue is the 4 letter word PONG
I've seen this crossword clue in The Guardian
P
O
N
G
Buddy explains!

The straight part
We know that "Nasty smell" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nasty smell = pong.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 PONG mean?
PONG noun- A stench, a bad smell.
- To stink, to smell bad.
- To deliver a line of a play in an arch, suggestive or unnatural way, so as to draw undue attention to it.
- A packet sent in reply to a ping, thereby indicating the presence of a host.
- A set of three identical tiles.