The most common and most likely answer to this crossword clue is the 5 plus 4 plus 3 letter word UNDER ONES HAT
I've seen this crossword clue in The Times
U
N
D
E
R
O
N
E
S
H
A
T
Buddy explains!
The straight part
We know that "apparently, in secret storage space" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case apparently, in secret storage space = under ones hat.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.