The most common and most likely answer to this crossword clue is the 5 plus 5 letter word AFTER SHAVE
I've seen this crossword clue in The Daily Telegraph
A
F
T
E
R
S
H
A
V
E
Buddy explains!
The straight part
We know that "fragrant thing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fragrant thing = after shave.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 AFTER SHAVE mean?
AFTER SHAVE noun- A lotion, gel, or liquid used after finishing shaving