The most common and most likely answer to this crossword clue is the 9 letter word ASTROLOGY
I've seen this crossword clue in The Guardian
A
S
T
R
O
L
O
G
Y
Buddy explains!

The straight part
We know that "predictions" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case predictions = astrology.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 ASTROLOGY mean?
ASTROLOGY noun- Divination about human affairs or natural phenomena from the relative positions of celestial bodies.