The most common and most likely answer to this crossword clue is the 4 letter word MUSK
I've seen this crossword clue in The Daily Telegraph
M
U
S
K
More clues leading to the result MUSK
Buddy explains!

The straight part
We know that "a strong perfume" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a strong perfume = musk.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 MUSK mean?
MUSK noun- A greasy secretion with a powerful odour, produced in a glandular sac of the male musk deer and used in the manufacture of perfumes.
- A similar secretion produced by the otter and the civet.
- A synthetic organic compound used as a substitute for the above.
- The odour of musk.
- The musk deer (genus Moschus).
- The musk plant (Mimulus moschatus).
- A plant of the genus Erodium (Erodium moschatum); the musky heronsbill.
- A plant of the genus Muscari; grape hyacinth.
- The scent of human genitalia when aroused or unwashed.
- To perfume with musk.