The most common and most likely answer to this crossword clue is the 10 letter word OTHERWORLD
O
T
H
E
R
W
O
R
L
D
More clues leading to the result OTHERWORLD
Buddy explains!

The straight part
We know that "spiritual life elsewhere" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case spiritual life elsewhere = otherworld.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 OTHERWORLD mean?
OTHERWORLD noun- A world beyond death; an afterlife.
- A world other than the everyday world.
- Mythical abode of otherworldy beings.