The most common and most likely answer to this crossword clue is the 5 letter word VIRTU
I've seen this crossword clue in Financial Times
V
I
R
T
U
More clues leading to the result VIRTU
Buddy explains!

The straight part
We know that "connoisseurship" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case connoisseurship = virtu.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 VIRTU mean?
VIRTU noun- The fine arts as a subject of study or expertise; understanding of arts and antiquities.
- Objets d'art collectively.
- Especially with reference to the writings of Machiavelli (1469–1527): the requisite qualities for political or military success; vitality, determination; power.
- Moral worth; virtue, virtuousness.