The most common and most likely answer to this crossword clue is the 8 plus 7 letter word CARDINAL NUMBERS
I've seen this crossword clue in Financial Times
C
A
R
D
I
N
A
L
N
U
M
B
E
R
S
Buddy explains!
The straight part
We know that "Figures showing how many/anaesthetists in the Vatican?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case figures showing how many/anaesthetists in the vatican? = cardinal numbers.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.