The most common and most likely answer to this crossword clue is the 4 plus 5 letter word LAST RITES
I've seen this crossword clue in The Times
L
A
S
T
R
I
T
E
S
More clues leading to the result LAST RITES
- Girl keeping dull church observances towards the end
- Girl accepting uninspired services at the end
- Tired girl's taken in procedure near the end.
- Girl closes hackneyed religious ceremony
- Leaving ceremony is routine, girl admits
- Young woman embracing facile ceremony
- Girl catching banal ceremony before the end
- Unction etc is commonplace in a girl
- Speech from minister before one goes to the dispatch box?
- Miss receiving uninspired blessing one’s dying to hear?
Buddy explains!

The straight part
We know that "church observances towards the end" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case church observances towards the end = last rites.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.