The most common and most likely answer to this crossword clue is the 5 plus 10 letter word SIMON BOCCANEGRA
I've seen this crossword clue in The Guardian
S
I
M
O
N
B
O
C
C
A
N
E
G
R
A
More clues leading to the result SIMON BOCCANEGRA
Buddy explains!
The straight part
We know that "top Genoese" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case top genoese = simon boccanegra.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.