Connoisseurship is a kind of expertise in a particular subject, especially an area of art. After years of listening to rockabilly music, your dad's connoisseurship of early rock-and-roll is unmatched.
When someone is a connoisseur, they have a deep love and extensive knowledge of a subject that's considered to be a matter of taste. Connoisseurship is what a connoisseur possesses. Your sister, for example, has devoted years to her connoisseurship of French New Wave film, while you've turned your attention to the connoisseurship of fine cheeses. This word comes from the Old French conoisseor, "an expert or judge," and its Latin source cognoscere, "to get to know."