The most common and most likely answer to this crossword clue is the 9 letter word GUSTATION
I've seen this crossword clue in The Times
G
U
S
T
A
T
I
O
N
Buddy explains!
The straight part
We know that "faculty of distinction" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case faculty of distinction = gustation.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 GUSTATION mean?
GUSTATION noun- The act of tasting.
- The ability to taste flavors; the sense of taste.