The most common and most likely answer to this crossword clue is the 10 letter word ANTECHAPEL
I've seen this crossword clue in Financial Times
A
N
T
E
C
H
A
P
E
L
Buddy explains!
The straight part
We know that "western transept" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case western transept = antechapel.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 ANTECHAPEL mean?
ANTECHAPEL noun- The outer part of the west end of a chapel.