The most common and most likely answer to this crossword clue is the 14 letter word RASTAFARIANISM
I've seen this crossword clue in The Times
R
A
S
T
A
F
A
R
I
A
N
I
S
M
More clues leading to the result RASTAFARIANISM
Buddy explains!

The straight part
We know that "Practice of one type of religious person" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case practice of one type of religious person = rastafarianism.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.