The most common and most likely answer to this crossword clue is the 10 plus 5 letter word LATTER-DAY SAINT
I've seen this crossword clue in The Times
L
A
T
T
E
R
-
D
A
Y
S
A
I
N
T
Buddy explains!
The straight part
We know that "US church member" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case us church member = latter-day saint.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.