The most common and most likely answer to this crossword clue is the 8 letter word TEMPORAL
I've seen this crossword clue in The Daily Telegraph
T
E
M
P
O
R
A
L
More clues leading to the result TEMPORAL
- Supply worker has spoken — about time
- Like some in Lords, having spoken with a small degree of heat to start with
- . Lay odds of trek maps being seen before test
- Johnson returns with nothing in bungled alert — about time
- Part-time worker’s said to be worldly
- Passing port to be drunk with meal
- The heartless member has spoken of such lords
- Tense, the compiler flipped, quietly spoken and profane
- Rhythm really oddly unspiritual
- Of time lords in Parliament?
Buddy explains!

The straight part
We know that "unspiritual" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unspiritual = temporal.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 TEMPORAL mean?
TEMPORAL noun- (chiefly in the plural) Anything temporal or secular; a temporality.
- (also grammar) Of or relating to time.
- Of limited time; transient; passing; not perpetual.
- Of or relating to the material world, as opposed to spiritual.
- Lasting a short time only.
- Civil or political, as distinguished from ecclesiastical.
- Either of the bones on the side of the skull, near the ears.
- Any of a reptile's scales on the side of the head between the parietal and supralabial scales, and behind the postocular scales.
- Of the temples of the head