The most common and most likely answer to this crossword clue is the 6 plus 2 plus 4 letter word CHAPEL OF REST
I've seen this crossword clue in The Guardian
C
H
A
P
E
L
O
F
R
E
S
T
Buddy explains!
The straight part
We know that "undertaker’s parlour" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case undertaker’s parlour = chapel of rest.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.