The most common and most likely answer to this crossword clue is the 16 letter word &ROGEN(ANDROGEN)
&
R
O
G
E
N
(
A
N
D
R
O
G
E
N
)
Buddy explains!
The straight part
We know that "synthetic sex hormone" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case synthetic sex hormone = &rogen(androgen).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.